WO2019144657A1 - Method for dynamically determining optimal number of insulating layers in transient thermal path of high-voltage cable - Google Patents
Method for dynamically determining optimal number of insulating layers in transient thermal path of high-voltage cable Download PDFInfo
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- the invention relates to the technical field of current carrying capacity calculation of high voltage cables, in particular to a method for dynamically determining the optimal number of insulation layers in a transient thermal path of a high voltage cable.
- the calculation of cable current carrying capacity mainly includes numerical solution and analytical method.
- the former includes finite element method and boundary element method, and the latter includes IEC 60287, IEC 60853, and heat path.
- the thermal path method needs to construct the transient thermal path model according to the cable structure size and physical property parameters and determine the parameters, and the treatment of the insulation layer is an extremely important part.
- Zhou Fan et al. used four different layering methods for the insulation layer in the transient thermal path model processing to explore the influence of layering type and layer number on the current carrying capacity calculation. It was found that the insulation layering can improve the calculation accuracy of the cable current carrying capacity. . However, the study only stayed at the qualitative level, and did not quantitatively give the optimal number of layers of insulation. Moreover, it did not analyze the influence of the change of the number of layers at different times on the current carrying capacity during the whole temperature rise process.
- the object of the present invention is to overcome the shortcomings and deficiencies of the prior art, and to provide a method for dynamically determining the optimal number of insulation layers in a transient thermal path of a high voltage cable, and not only a method for quantitatively determining the optimal number of layers of insulation, Moreover, the variation of the optimal number of layers in different temperature rise times is considered, and the purpose of dynamically and real-time determining the optimal number of layers in the transient thermal path of the high-voltage cable is realized.
- the object of the present invention is achieved by the following technical solution: a method for dynamically determining the optimal number of insulation layers in a transient thermal path of a high voltage cable, comprising the following steps:
- step S4 according to the mathematical model in step S2, using MATLAB to edit the calculation program;
- step S1 according to the calculation requirement, the high-voltage cable of the target model is selected as a calculation prototype, and parameters for determining the structure of each layer of the relevant cable include: size data, material properties, thermal conductivity, specific heat capacity, and resistivity.
- the step S201 is specifically:
- the transient thermal path model is based on the following assumptions: 1) the cable length is infinite relative to the cable radius, and the axial heat transfer is ignored for the long straight cable section; 2) in general laying Conditions, especially under experimental conditions, the external environment of the cable is uniform, the material of each layer of the cable is isotropic, and the center is symmetrical; 3) the heat capacity of each layer of material does not change with time space; 4) the inner and outer shielding layers are thin and thermal parameters Similar to the insulating layer, so the three are combined with the same layer of processing, 5) the dielectric loss is negligible in terms of relative conductor loss, and the sheath loss is ignored in the case of single-ended grounding;
- the cable body thermal path is simplified into a one-dimensional heat path model along the radial direction, while the insulation layer is treated by equal thickness stratification, the cable thermal path model is a distributed parameter transient thermal path model; and the setting: P represents the cable conductor Loss; n-3 indicates the number of layers of the insulation layer; T 1 indicates the cable conductor temperature; T 2 -T n-3 indicates the cable insulation layer, including the inner and outer shield delamination temperatures; T n-2 indicates the winding temperature T n-1 denotes the temperature of the air gap layer; T n denotes the temperature of the aluminum sheath; T o denotes the temperature of the cable skin; C 1 ' denotes the heat capacity of the cable conductor; C 1 ', C 2 - C n-3 denote the insulation of the cable , containing the heat capacity of each layer of the inner and outer shield layers; C n-2 represents the heat capacity around the cladding; C n-1 represents the heat capacity of the air gap layer; C n
- step S202 is specifically:
- T [T 1 T 2 T 3 L T n ] T
- the step S301 is specifically:
- the time-invariant parameters include the heat capacity and thermal resistance of each layer of material, and the heat capacity of each layer is calculated according to the IEC 60287 standard;
- d 2 is the calculated layer outer diameter
- d 1 is the calculated layer inner diameter
- ⁇ is the calculated volumetric heat capacity of the layer material
- d 1 represents the inner diameter of the calculation layer
- d 2 represents the outer diameter of the calculation layer
- step S302 is specifically:
- the time-varying parameters include conductor loss and cable surface temperature, wherein the cable surface temperature is measured by the thermocouple in real time, and the conductor loss changes with the change of the conductor resistance;
- the conductor loss per unit length is calculated as follows:
- P is the heating power of the conductor
- I is the load current
- r is the AC resistance per unit length of the conductor
- r is the alternating current resistance of the conductor of unit length
- r' is the direct current resistance of the conductor of unit length
- Y s is the skin effect factor
- Y p is the adjacent effect factor
- r 0 is the DC resistance of the cable conductor per unit length at 20 ° C
- ⁇ is the temperature coefficient of resistance of the conductor
- ⁇ is the operating temperature
- k s is the empirical value
- f is the current frequency
- the step S4 is specifically: according to the equations listed in the series of nodes and the calculation method of each parameter thereof, the calculation program of the matrix A, B, and P and the solution program of the differential equations are edited by using MATLAB software.
- step S5 is specifically:
- Step 1 Select a certain moment as the starting point of calculation, import the calculation parameters at the moment, and proceed to the next step;
- Step 2 Set the number of layers to 1 layer, calculate the conductor temperature value T 11 at this time, and proceed to the next step;
- Step 3 Set the number of layers to 2 layers, calculate the conductor temperature value T 12 at this time, calculate the rate of change of temperature with the number of layers compared with the previous layer, and take the absolute value
- Step 5 Set the number of layers to i, calculate the conductor temperature value T 1i at this time, calculate the rate of change of temperature with the number of layers compared with the previous layer, and take the absolute value
- step S6 is specifically: step S5 determines the conductor temperature calculation result under the optimal layer number as the conductor temperature import value calculated at the next time, and then imports the skin temperature value at the next moment, and the other imported parameters remain. Without changing, the steps in step S5 are repeated to obtain the optimum number of layers of the insulating layer at the next moment.
- the step S7 is specifically: the calculation of the conductor temperature at each next time is based on the calculation result of the previous time, and the steps in the step S5 and the step S6 are continuously repeated to obtain the insulation at different times during the whole temperature rise process.
- the optimal number of layers in the layer that is, the optimal number of layers of the insulating layer in the transient hot path of the high-voltage cable is determined in real time.
- the present invention has the following advantages and beneficial effects:
- the invention optimizes the treatment of the insulation layer in the transient hot road model of the high-voltage cable, and can obtain a more optimized transient thermal path model. Considering the time-varying factor, the method for determining the optimal stratification of the insulation layer is given and the model is real-time. The correction feature lays an important foundation for accurate calculation of cable current carrying capacity.
- Figure 1 is a schematic cross-sectional view of a high voltage cable of an embodiment
- FIG. 2 is a schematic diagram of a distributed parameter transient thermal path model of an embodiment.
- a method for dynamically determining the optimal number of layers of insulation in a transient thermal path of a high voltage cable includes the following steps:
- S1 select the required high-voltage cable, determine its size and material properties of each layer.
- the general structure diagram of the high-voltage cable is shown in Figure 1.
- the data is determined to determine the dimensional data, material properties, thermal conductivity, specific heat capacity and resistivity of the relevant layers of the relevant cable. and many more.
- the transient thermal path model is based on the following assumptions: 1) the cable length is infinite relative to the cable radius, and the axial heat transfer is ignored for the long straight cable section; 2) in general laying Conditions, especially under experimental conditions, the external environment of the cable is uniform, the material of each layer of the cable is isotropic, and the center is symmetrical; 3) the heat capacity of each layer of material does not change with time space; 4) the inner and outer shielding layers are thin and thermal parameters Similar to the insulating layer, so the three are combined with the same layer of processing, 5) relative to the loss of the conductor, the dielectric loss is negligible, and the sheath loss is ignored in the case of single-ended grounding. Based on the above assumptions, the cable body thermal path is simplified into a one-dimensional heat path model along the radial direction, while the insulating layer is processed by equal thickness stratification, and the distributed parameter transient thermal path model is shown in FIG. 2 .
- T 1 represents the cable conductor temperature, ° C
- T 2 - T n-3 represents the cable insulation layer (including the inner and outer shield) layers
- the thermal path has an analysis method similar to that of the circuit.
- the node equations are written for each node in the thermal path and converted into a matrix representation:
- T [T 1 T 2 T 3 L T n ] T
- the time-invariant parameters include the heat capacity and thermal resistance of each layer of material, and the heat capacity of each layer is calculated according to the IEC 60287 standard.
- d 1 represents the inner diameter of the calculated layer, mm
- d 2 represents the outer diameter of the calculated layer, mm.
- time-varying parameters include conductor loss and cable surface temperature, where the cable surface temperature is measured in real time by a thermocouple, and the conductor loss changes as the conductor resistance changes.
- the conductor loss per unit length is calculated as follows:
- k s is the empirical value, which can be taken as 1 for a dry copper round wire
- f is the current frequency, Hz.
- Step 1 Select a certain moment as the starting point of calculation, and introduce the calculation parameters of the conductor temperature, the skin temperature, the thermal resistivity of each layer of material and the specific heat capacity at the moment, and proceed to the next step;
- Step 2 Set the number of layers to 1 layer, calculate the conductor temperature value T 11 at this time, and proceed to the next step;
- Step 3 Set the number of layers to 2 layers, calculate the conductor temperature value T 12 at this time, calculate the rate of change of temperature with the number of layers compared with the previous layer, and take the absolute value
- Step 5 Set the number of layers to i, calculate the conductor temperature value T 1i at this time, calculate the rate of change of temperature with the number of layers compared with the previous layer, and take the absolute value
- step S5 the conductor temperature calculation result under the optimal layer number is determined as the conductor temperature introduction value calculated at the next time, and then the skin temperature value at the next moment is imported, and the other imported parameters remain unchanged, and step S5 is repeated to obtain the next step.
- the optimal number of layers of insulation at a time is determined as the conductor temperature introduction value calculated at the next time, and then the skin temperature value at the next moment is imported, and the other imported parameters remain unchanged, and step S5 is repeated to obtain the next step.
- the optimal number of layers of insulation at a time is determined as the conductor temperature introduction value calculated at the next time, and then the skin temperature value at the next moment is imported, and the other imported parameters remain unchanged, and step S5 is repeated to obtain the next step.
- the optimal number of layers of insulation at a time is determined as the conductor temperature introduction value calculated at the next time, and then the skin temperature value at the next moment is imported, and the other imported parameters remain unchanged, and step S5 is repeated to obtain the next step.
- the calculation of the conductor temperature at each next moment is based on the calculation result at the previous moment. Repeating steps S5 and S6 are repeated to obtain the optimal number of layers of the insulation layer at different times during the entire temperature rise process, that is, real-time and dynamic. Determine the optimal number of layers of insulation in the transient thermal path of the high voltage cable.
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Abstract
A method for dynamically determining an optimal number of insulating layers in a transient thermal path of a high-voltage cable, comprising the following steps: S1, choosing a high-voltage cable needed; S2, building a transient thermal path model and corresponding mathematical model of the cable body; S3, determining each parameter in the models; S4, editing a calculation program in the mathematical model in S1; S5, importing each model parameter, calculating a temperature value of a conductor in different numbers of layers at the same moment, and solving a change rate of the conductor temperature along with the number of layers, wherein when the change rate reaches a lower limit of a set change rate, the number of layers at this time is the optimal number of layers; S6, determining the optimal number of insulating layers at the next moment based on a calculation result in S5; and S7, repeating S5 and S6 to obtain a real-time optimal number of of insulating layers in a transient thermal path of the high-voltage cable. By means of the method, a better transient thermal path model can be obtained, and the model has a real-time correction property, laying an important foundation for accurate calculation of the carrying capacity of a cable.
Description
本发明涉及高压电缆载流量计算技术领域,特别涉及一种动态确定高压电缆暂态热路中绝缘最佳分层数的方法。The invention relates to the technical field of current carrying capacity calculation of high voltage cables, in particular to a method for dynamically determining the optimal number of insulation layers in a transient thermal path of a high voltage cable.
随着城市用电量的大幅度增加,同时为了提高城市空间的利用率,城区输电网广泛采用大容量的电缆线路送电。近年来,中心城区部分电缆线路逐渐接近甚至超过了其设计载流量,严重威胁电力系统的安全运行。扩建电缆线路成本高,周期长,并且受到征地等问题的制约,短期内无法解决线路过负荷问题。因此,电缆线路的增容势在必行,而增容的基础是准确计算电缆线路的载流量。With the large increase in electricity consumption in cities, and in order to improve the utilization of urban space, urban transmission networks use large-capacity cable lines to transmit electricity. In recent years, some cable lines in the central city have gradually approached or even exceeded their designed current carrying capacity, seriously threatening the safe operation of the power system. The expansion of cable lines is costly, long-term, and subject to land acquisition and other issues, and the line overload problem cannot be solved in a short period of time. Therefore, the expansion of cable lines is imperative, and the basis for capacity expansion is to accurately calculate the current carrying capacity of cable lines.
目前,电缆载流量的计算主要有数值解法和解析法,前者包括有限元法、边界元法等,后者包括IEC 60287、IEC 60853、热路等方法。其中热路法在计算暂态过程时需要根据电缆结构尺寸、物性参数构建暂态热路模型并确定各参数,而绝缘层的处理则是极其重要的一环。At present, the calculation of cable current carrying capacity mainly includes numerical solution and analytical method. The former includes finite element method and boundary element method, and the latter includes IEC 60287, IEC 60853, and heat path. In the calculation of the transient process, the thermal path method needs to construct the transient thermal path model according to the cable structure size and physical property parameters and determine the parameters, and the treatment of the insulation layer is an extremely important part.
周凡等人在暂态热路模型处理中对绝缘层采用4种不同的分层方法,探究分层类型及分层数对载流量计算影响,发现绝缘分层能提高电缆载流量的计算精度。但该研究只停留在定性的层面,并没有定量给出绝缘的最佳分层数,更没有分析在整个温升过程中不同时刻分层数变化对载流量计算的影响。Zhou Fan et al. used four different layering methods for the insulation layer in the transient thermal path model processing to explore the influence of layering type and layer number on the current carrying capacity calculation. It was found that the insulation layering can improve the calculation accuracy of the cable current carrying capacity. . However, the study only stayed at the qualitative level, and did not quantitatively give the optimal number of layers of insulation. Moreover, it did not analyze the influence of the change of the number of layers at different times on the current carrying capacity during the whole temperature rise process.
发明内容Summary of the invention
本发明的目的在于克服现有技术的缺点与不足,提供一种动态确定高压电缆暂态热路中绝缘最佳分层数的方法,不仅给出了定量确定绝缘最佳分层数的方法,而且还考虑了不同温升时刻最佳分层数的变化,实现动态、实时确定高压电缆暂态热路中绝缘层最佳分层数的目的。The object of the present invention is to overcome the shortcomings and deficiencies of the prior art, and to provide a method for dynamically determining the optimal number of insulation layers in a transient thermal path of a high voltage cable, and not only a method for quantitatively determining the optimal number of layers of insulation, Moreover, the variation of the optimal number of layers in different temperature rise times is considered, and the purpose of dynamically and real-time determining the optimal number of layers in the transient thermal path of the high-voltage cable is realized.
本发明的目的通过以下的技术方案实现:一种动态确定高压电缆暂态热路中绝缘最佳分层数的方法,包括以下步骤:The object of the present invention is achieved by the following technical solution: a method for dynamically determining the optimal number of insulation layers in a transient thermal path of a high voltage cable, comprising the following steps:
S1、选择所需高压电缆,确定其尺寸及各层材料物性参数;S1, selecting a required high-voltage cable, determining its size and physical property parameters of each layer;
S2、构建电缆本体暂态热路模型及对应的数学模型,该步骤具体为:S2, constructing a cable body transient thermal path model and a corresponding mathematical model, the steps are specifically:
S201、构建电缆本体暂态热路模型;S201, constructing a transient thermal path model of the cable body;
S202、构建热路模型对应的数学模型;S202. Construct a mathematical model corresponding to the heat path model;
S3、确定暂态热路模型中各参数,该步骤具体为:S3. Determine each parameter in the transient thermal path model, and the step is specifically:
S301、时不变参数的确定;S301, determining the time-invariant parameter;
S302、时变参数的确定;S302, determining a time-varying parameter;
S4、根据步骤S2中的数学模型,采用MATLAB编辑计算程序;S4, according to the mathematical model in step S2, using MATLAB to edit the calculation program;
S5、导入各模型参数,利用循环语句,计算某一时刻不同分层数下导体的温度值,求解导体温度随分层数的变化率,当变化率达到设定的变化率下限,此时分层数为最佳分层数;S5, importing each model parameter, using a loop statement, calculating the temperature value of the conductor under different layer numbers at a certain time, and solving the rate of change of the conductor temperature with the number of layers, when the rate of change reaches the lower limit of the set rate of change, at this time, layering The number is the optimal number of layers;
S6、以S5中计算结果为基础,并重复S5中的步骤,确定下一时刻的绝缘层最佳分层数;S6, based on the calculation result in S5, and repeating the steps in S5 to determine the optimal number of layers of the insulation layer at the next moment;
S7、重复S5、S6,即可得到高压电缆暂态热路中绝缘层实时最佳分层数。S7, repeat S5, S6, the real-time optimal stratification number of the insulation layer in the transient hot path of the high-voltage cable can be obtained.
优选的,步骤S1中:根据计算需要,选择对象型号的高压电缆作为计算原型,确定相关电缆各层结构的参数包括:尺寸数据、材料特性、导热率、比热容、电阻率。Preferably, in step S1: according to the calculation requirement, the high-voltage cable of the target model is selected as a calculation prototype, and parameters for determining the structure of each layer of the relevant cable include: size data, material properties, thermal conductivity, specific heat capacity, and resistivity.
优选的,所述步骤S201具体为:Preferably, the step S201 is specifically:
根据电缆线路和各层材料的特点,构建暂态热路模型基于以下假设:1)相对电缆半径,电缆线路长度无限大,对于长直电缆段,忽略其轴向传热;2)在一般敷设条件特别是实验条件下,电缆外部环境均匀,电缆各层材料各向同性,并且中心对称;3)各层材料的热容热阻不随时间空间而变化;4)内外屏蔽层很薄且热参数与绝缘层相似,因此三者合并同一层处理,5)相对导体损耗而言,介质损耗忽略不计,单端接地情况下忽略护套损耗;According to the characteristics of the cable line and the material of each layer, the transient thermal path model is based on the following assumptions: 1) the cable length is infinite relative to the cable radius, and the axial heat transfer is ignored for the long straight cable section; 2) in general laying Conditions, especially under experimental conditions, the external environment of the cable is uniform, the material of each layer of the cable is isotropic, and the center is symmetrical; 3) the heat capacity of each layer of material does not change with time space; 4) the inner and outer shielding layers are thin and thermal parameters Similar to the insulating layer, so the three are combined with the same layer of processing, 5) the dielectric loss is negligible in terms of relative conductor loss, and the sheath loss is ignored in the case of single-ended grounding;
基于以上假设,电缆本体热路简化成沿着径向的一维热路模型,同时绝缘层采用等厚度分层处理,电缆热路模型为分布参数暂态热路模型;设置:P表示电缆导体损耗;n-3表示绝缘层分层数;T
1表示电缆导体温度;T
2—T
n-3表示电缆绝缘层,含内、外屏蔽各分层温度;T
n-2 表示绕包带温度;T
n-1表示气隙层温度;T
n表示铝护套温度;T
o表示电缆表皮温度;C
1'表示电缆导体热容;C
1″、C
2—C
n-3表示电缆绝缘层,含内、外屏蔽层各分层热容;C
n-2表示绕包层热容;C
n-1表示气隙层热容;C
n'表示铝护套热容;C
n″表示外护套热容;R
1—R
n-3表示电缆绝缘层,含内、外屏蔽各分层热阻;R
n-2表示绕包层热阻;R
n-1表示气隙层热阻;R
n表示外护套热阻。
Based on the above assumptions, the cable body thermal path is simplified into a one-dimensional heat path model along the radial direction, while the insulation layer is treated by equal thickness stratification, the cable thermal path model is a distributed parameter transient thermal path model; and the setting: P represents the cable conductor Loss; n-3 indicates the number of layers of the insulation layer; T 1 indicates the cable conductor temperature; T 2 -T n-3 indicates the cable insulation layer, including the inner and outer shield delamination temperatures; T n-2 indicates the winding temperature T n-1 denotes the temperature of the air gap layer; T n denotes the temperature of the aluminum sheath; T o denotes the temperature of the cable skin; C 1 ' denotes the heat capacity of the cable conductor; C 1 ', C 2 - C n-3 denote the insulation of the cable , containing the heat capacity of each layer of the inner and outer shield layers; C n-2 represents the heat capacity around the cladding; C n-1 represents the heat capacity of the air gap layer; C n ' represents the heat capacity of the aluminum sheath; C n ′′ indicates the outside Sheath heat capacity; R 1 —R n-3 denotes the cable insulation layer, including the inner and outer shields of each layer of thermal resistance; R n-2 denotes the thermal resistance of the cladding layer; R n-1 denotes the thermal resistance of the air gap layer; R n represents the thermal resistance of the outer sheath.
进一步的,所述步骤S202具体为:Further, the step S202 is specifically:
对热路中的每个节点列写节点方程,并转化为矩阵表达形式:Write a node equation for each node in the heat path and convert it into a matrix representation:
其中,C
1=C
1'+C
1″,C
n=C
n'+C
n″,各矩阵如下:
Where C 1 =C 1 '+C 1 ′′, C n =C n '+C n ′′, and the matrices are as follows:
T=[T
1 T
2 T
3 L T
n]
T
T=[T 1 T 2 T 3 L T n ] T
优选的,所述步骤S301具体为:Preferably, the step S301 is specifically:
在暂态热路模型中,基于假设,时不变参数包括各层材料的热容、热阻,各层热容热阻以IEC 60287标准计算;In the transient thermal path model, based on the assumption, the time-invariant parameters include the heat capacity and thermal resistance of each layer of material, and the heat capacity of each layer is calculated according to the IEC 60287 standard;
单位长度热容计算公式如下:The formula for calculating the heat capacity per unit length is as follows:
式中:d
2为计算层外径;d
1为计算层内径;δ为计算层材料的体积热容;
Where: d 2 is the calculated layer outer diameter; d 1 is the calculated layer inner diameter; δ is the calculated volumetric heat capacity of the layer material;
单位长度热阻计算公式如下:The formula for calculating the thermal resistance per unit length is as follows:
式中:d
1表示计算层内径;d
2表示计算层外径。
Where: d 1 represents the inner diameter of the calculation layer; d 2 represents the outer diameter of the calculation layer.
优选的,所述步骤S302具体为:Preferably, the step S302 is specifically:
在暂态热路模型中,时变参数包括导体损耗和电缆表面温度,其中电缆表面温度由热电偶实时测量所得,导体损耗随着导体电阻的变化而变化;In the transient thermal path model, the time-varying parameters include conductor loss and cable surface temperature, wherein the cable surface temperature is measured by the thermocouple in real time, and the conductor loss changes with the change of the conductor resistance;
单位长度导体损耗计算如下:The conductor loss per unit length is calculated as follows:
P=I
2r
P=I 2 r
式中:P为导体的发热功率;I为负荷电流;r为单位长度导体交流电阻;Where: P is the heating power of the conductor; I is the load current; r is the AC resistance per unit length of the conductor;
导体工作温度下单位长度的交流电阻计算公式:Calculation formula of AC resistance per unit length at conductor operating temperature:
r=r′(1+Y
s+Y
p)
r=r'(1+Y s +Y p )
式中:r为单位长度导体的交流电阻;r′为单位长度导体的直流电阻;Y
s为集肤效应因数;Y
p为邻近效应因数;
Where: r is the alternating current resistance of the conductor of unit length; r' is the direct current resistance of the conductor of unit length; Y s is the skin effect factor; Y p is the adjacent effect factor;
单位长度导体的直流电阻计算公式:The formula for calculating the DC resistance of a conductor per unit length:
r′=r
0×[1+α(θ-20)]
r'=r 0 ×[1+α(θ-20)]
式中:r
0为20℃时单位长度电缆导体的直流电阻;α为导体的电阻温度系数;θ为工作温度;
Where: r 0 is the DC resistance of the cable conductor per unit length at 20 ° C; α is the temperature coefficient of resistance of the conductor; θ is the operating temperature;
集肤效应因数Y
s计算公式:
Skin effect factor Y s calculation formula:
式中:k
s为经验值;f为电流频率。
Where: k s is the empirical value; f is the current frequency.
优选的,所述步骤S4具体为:根据系列节点所列方程组以及其中各参数的计算方法,采用MATLAB软件,编辑矩阵A、B、P的计算程序和微分方程组的求解程序。Preferably, the step S4 is specifically: according to the equations listed in the series of nodes and the calculation method of each parameter thereof, the calculation program of the matrix A, B, and P and the solution program of the differential equations are edited by using MATLAB software.
优选的,所述步骤S5具体为:Preferably, the step S5 is specifically:
步骤1:选取某一时刻作为计算起点,导入此刻的计算参数,进入下一步骤;Step 1: Select a certain moment as the starting point of calculation, import the calculation parameters at the moment, and proceed to the next step;
步骤2:设置分层数为1层,计算此时导体温度值T
11,进入下一步骤;
Step 2: Set the number of layers to 1 layer, calculate the conductor temperature value T 11 at this time, and proceed to the next step;
步骤3:设置分层数为2层,计算此时导体温度值T
12,较上一分层数计算温度随分层数的变化率,并取其绝对值|T
11-T
12|,若|T
11-T
12|小于设定值,则绝缘层的最佳分层数为2,结束,否则进入下一步骤;
Step 3: Set the number of layers to 2 layers, calculate the conductor temperature value T 12 at this time, calculate the rate of change of temperature with the number of layers compared with the previous layer, and take the absolute value |T 11 -T 12 |, if | T 11 -T 12 | is less than the set value, then the optimal number of layers of the insulating layer is 2, ending, otherwise it proceeds to the next step;
步骤4:取分层数变量i=3,进入下一步;Step 4: Take the layer number variable i=3 and proceed to the next step;
步骤5:设置分层数为i,计算此时导体温度值T
1i,较上一分层数计算温度随分层数的变化率,并取其绝对值|T
1(i-1)-T
1i|,若|T
1(i-1)-T
1i|小于设定值,则绝缘层的最佳分层数为i,结束,否则进入下一步骤;
Step 5: Set the number of layers to i, calculate the conductor temperature value T 1i at this time, calculate the rate of change of temperature with the number of layers compared with the previous layer, and take the absolute value |T 1(i-1) -T 1i |, if |T 1(i-1) -T 1i | is less than the set value, the optimal number of layers of the insulating layer is i, end, otherwise proceed to the next step;
步骤6:i=i+1,返回步骤5。Step 6: i=i+1, return to step 5.
优选的,所述步骤S6具体为:步骤S5确定最佳分层数下的导体温度计算结果作为下一时刻计算的导体温度导入值,再导入下一时刻的表皮温度值,其他导入的参数保持不变,重复步骤S5中各步骤,得到下一时刻绝缘层的最佳分层数。Preferably, the step S6 is specifically: step S5 determines the conductor temperature calculation result under the optimal layer number as the conductor temperature import value calculated at the next time, and then imports the skin temperature value at the next moment, and the other imported parameters remain. Without changing, the steps in step S5 are repeated to obtain the optimum number of layers of the insulating layer at the next moment.
优选的,所述步骤S7具体为:每下一时刻导体温度的计算均以上一时刻的计算结果为基础,不断重复步骤S5和步骤S6中各步骤,即可得到整个温升过程中不同时刻绝缘层的最佳分层数,也就是实时确定高压电缆暂态热路中绝缘层最佳分层数。Preferably, the step S7 is specifically: the calculation of the conductor temperature at each next time is based on the calculation result of the previous time, and the steps in the step S5 and the step S6 are continuously repeated to obtain the insulation at different times during the whole temperature rise process. The optimal number of layers in the layer, that is, the optimal number of layers of the insulating layer in the transient hot path of the high-voltage cable is determined in real time.
本发明与现有技术相比,具有如下优点和有益效果:Compared with the prior art, the present invention has the following advantages and beneficial effects:
本发明优化高压电缆暂态热路模型中的绝缘层处理,能得到更优化的暂态热路模型,考虑时变因素的同时,给出确定绝缘层最佳分层的方法并且使模型具有实时修正特性,为电缆载流量的准确计算打下重要基础。The invention optimizes the treatment of the insulation layer in the transient hot road model of the high-voltage cable, and can obtain a more optimized transient thermal path model. Considering the time-varying factor, the method for determining the optimal stratification of the insulation layer is given and the model is real-time. The correction feature lays an important foundation for accurate calculation of cable current carrying capacity.
图1是实施例高压电缆横截面示意图;Figure 1 is a schematic cross-sectional view of a high voltage cable of an embodiment;
图2是实施例分布参数暂态热路模型示意图。2 is a schematic diagram of a distributed parameter transient thermal path model of an embodiment.
下面结合实施例及附图对本发明作进一步详细的描述,但本发明的实施方式不限于此。The present invention will be further described in detail below with reference to the embodiments and drawings, but the embodiments of the present invention are not limited thereto.
实施例1Example 1
一种动态确定高压电缆暂态热路中绝缘最佳分层数的方法,包括下列步骤:A method for dynamically determining the optimal number of layers of insulation in a transient thermal path of a high voltage cable includes the following steps:
S1、选择所需高压电缆,确定其尺寸及各层材料物性参数。S1, select the required high-voltage cable, determine its size and material properties of each layer.
根据计算需要,选择某种型号的高压电缆作为计算原型,高压电缆的一般结构示意图如附图1所示,查阅资料确定相关电缆各层结构的尺寸数据、材料特性、导热率、比热容、电阻率等等。According to the calculation needs, select a certain type of high-voltage cable as the calculation prototype. The general structure diagram of the high-voltage cable is shown in Figure 1. The data is determined to determine the dimensional data, material properties, thermal conductivity, specific heat capacity and resistivity of the relevant layers of the relevant cable. and many more.
S2、构建电缆本体暂态热路模型及对应的数学模型。S2. Construct a transient thermal path model of the cable body and a corresponding mathematical model.
S201、构建电缆本体暂态热路模型;S201, constructing a transient thermal path model of the cable body;
根据电缆线路和各层材料的特点,构建暂态热路模型基于以下假设:1)相对电缆半径,电缆线路长度无限大,对于长直电缆段,忽略其轴向传热;2)在一般敷设条件特别是实验条件下,电缆外部环境均匀,电缆各层材料各向同性,并且中心对称;3)各层材料的热容热阻不随时间空间而变化;4)内外屏蔽层很薄且热参数与绝缘层相似,因此三者合并同一层处理,5)相对导体损耗而言,介质损耗忽略不计,单端接地情况下忽略护套损耗。基于以上假设,电缆本体热路简化成沿着径向的一维热路模型,同时绝缘层采用等厚度分层处理,分布参数暂态热路模型如附图2所示。According to the characteristics of the cable line and the material of each layer, the transient thermal path model is based on the following assumptions: 1) the cable length is infinite relative to the cable radius, and the axial heat transfer is ignored for the long straight cable section; 2) in general laying Conditions, especially under experimental conditions, the external environment of the cable is uniform, the material of each layer of the cable is isotropic, and the center is symmetrical; 3) the heat capacity of each layer of material does not change with time space; 4) the inner and outer shielding layers are thin and thermal parameters Similar to the insulating layer, so the three are combined with the same layer of processing, 5) relative to the loss of the conductor, the dielectric loss is negligible, and the sheath loss is ignored in the case of single-ended grounding. Based on the above assumptions, the cable body thermal path is simplified into a one-dimensional heat path model along the radial direction, while the insulating layer is processed by equal thickness stratification, and the distributed parameter transient thermal path model is shown in FIG. 2 .
其中:P表示电缆导体损耗,W;n-3表示绝缘层分层数;T
1表示电缆导体温度,℃;T
2—T
n-3表示电缆绝缘层(含内、外屏蔽)各分层温度,℃;T
n-2表示绕包带温度,℃;T
n-1表示气隙层温度,℃;T
n表示铝护套温度,℃;T
o表示电缆表皮温度,℃;C
1'表示电缆导体热容,J/K;C
1″、C
2—C
n-3表示电缆绝缘层(含内、外屏蔽层)各分层热容,J/K;C
n-2表示绕包层热容,J/K;C
n-1表示气隙层热容,J/K;C
n'表示铝护套热容,J/K;C
n″表示外护套热容,J/K;R
1—R
n-3表示电缆绝缘层(含内、外屏蔽)各分层热阻,K·m/W;R
n-2表示绕包层热阻,K·m/W;R
n-1表示气隙层热阻,K·m/W;R
n表示外护套热阻,K·m/W。
Where: P represents the cable conductor loss, W; n-3 represents the number of layers of the insulation layer; T 1 represents the cable conductor temperature, ° C; T 2 - T n-3 represents the cable insulation layer (including the inner and outer shield) layers Temperature, °C; T n-2 represents the wrapping temperature, ° C; T n-1 represents the air gap temperature, ° C; T n represents the aluminum sheath temperature, ° C; T o represents the cable skin temperature, ° C; C 1 ' Indicates the heat capacity of the cable conductor, J/K; C 1 ′′, C 2 — C n-3 represents the heat capacity of each layer of the cable insulation layer (including the inner and outer shield layers), J/K; C n-2 represents the package layer heat capacity, J / K; C n- 1 represents the heat capacity of air gap, J / K; C n 'represents aluminum sheath heat capacity, J / K; C n "represents the outer jacket heat capacity, J / K ; R 1 —R n-3 denotes the thermal resistance of each layer of the cable insulation layer (including inner and outer shields), K·m/W; R n-2 denotes the thermal resistance of the cladding, K·m/W; R n -1 represents the thermal resistance of the air gap layer, K·m/W; R n represents the thermal resistance of the outer sheath, K·m/W.
S202、构建热路模型对应的数学模型;S202. Construct a mathematical model corresponding to the heat path model;
热路具有与电路类似的分析方法,对热路中的每个节点列写节点方程,并转化为矩阵表达形式:The thermal path has an analysis method similar to that of the circuit. The node equations are written for each node in the thermal path and converted into a matrix representation:
其中,C
1=C
1'+C
1″,C
n=C
n'+C
n″,各矩阵如下:
Where C 1 =C 1 '+C 1 ′′, C n =C n '+C n ′′, and the matrices are as follows:
T=[T
1 T
2 T
3 L T
n]
T
T=[T 1 T 2 T 3 L T n ] T
S3、确定暂态热路模型中各参数。S3. Determine parameters in the transient thermal path model.
S301、时不变参数的确定S301, determination of time-invariant parameters
在暂态热路模型中,基于假设,时不变参数包括各层材料的热容、热阻,各层热容热阻以IEC 60287标准计算。In the transient thermal path model, based on the assumption, the time-invariant parameters include the heat capacity and thermal resistance of each layer of material, and the heat capacity of each layer is calculated according to the IEC 60287 standard.
单位长度热容计算公式如下:The formula for calculating the heat capacity per unit length is as follows:
式中:d
2为计算层外径,mm;d
1为计算层内径,mm;δ为计算层材料的体积热容,J/K·m
3。
Where: d 2 is the calculated layer outer diameter, mm; d 1 is the calculated layer inner diameter, mm; δ is the calculated volumetric heat capacity of the layer material, J / K · m 3 .
单位长度热阻计算公式如下:The formula for calculating the thermal resistance per unit length is as follows:
式中:d
1表示计算层内径,mm;d
2表示计算层外径,mm。
Where: d 1 represents the inner diameter of the calculated layer, mm; d 2 represents the outer diameter of the calculated layer, mm.
S302、时变参数的确定S302, determination of time-varying parameters
在暂态热路模型中,时变参数包括导体损耗和电缆表面温度,其中电缆表面温度由热电偶实时测量所得,导体损耗随着导体电阻的变化而变化。In the transient thermal path model, time-varying parameters include conductor loss and cable surface temperature, where the cable surface temperature is measured in real time by a thermocouple, and the conductor loss changes as the conductor resistance changes.
单位长度导体损耗计算如下:The conductor loss per unit length is calculated as follows:
P=I
2r
P=I 2 r
式中:P为导体的发热功率,W;I为负荷电流,A;r为单位长度导体交流电阻,Ω。Where: P is the heating power of the conductor, W; I is the load current, A; r is the AC resistance per unit length of conductor, Ω.
导体工作温度下单位长度的交流电阻计算公式:Calculation formula of AC resistance per unit length at conductor operating temperature:
r=r′(1+Y
s+Y
p)
r=r'(1+Y s +Y p )
式中:r为单位长度导体的交流电阻,Ω;r′为单位长度导体的直流电阻,Ω;Y
s为集肤效应因数;Y
p为邻近效应因数。
Where: r is the AC resistance of the conductor per unit length, Ω; r' is the DC resistance of the conductor per unit length, Ω; Y s is the skin effect factor; Y p is the adjacent effect factor.
单位长度导体的直流电阻计算公式:The formula for calculating the DC resistance of a conductor per unit length:
r′=r
0×[1+α(θ-20)]
r'=r 0 ×[1+α(θ-20)]
式中:r
0为20℃时单位长度电缆导体的直流电阻,Ω;α为导体的电阻温度系数,1/K;标准软铜:α=0.00393,该值取决于所使用的绝缘材料类型;θ为工作温度,K。
Where: r 0 is the DC resistance of the cable conductor per unit length at 20 ° C, Ω; α is the temperature coefficient of resistance of the conductor, 1 / K; standard soft copper: α = 0.00393, depending on the type of insulation material used; θ is the operating temperature, K.
集肤效应因数Y
s计算公式:
Skin effect factor Y s calculation formula:
式中:k
s为经验值,对于干燥的铜圆绞导线可取为1;f为电流频率,Hz。
Where: k s is the empirical value, which can be taken as 1 for a dry copper round wire; f is the current frequency, Hz.
S4、根据S1中的数学模型,采用MATLAB编辑计算程序;S4, according to the mathematical model in S1, using MATLAB to edit the calculation program;
根据系列节点所列方程组以及其中各参数的计算方法,采用MATLAB软件,编辑矩阵A、B、P的计算程序和微分方程组的求解程序。According to the equations listed in the series of nodes and the calculation methods of each parameter, the calculation program of matrix A, B, P and the solution program of differential equations are edited by MATLAB software.
S5、导入各模型参数,利用循环语句,计算某一时刻不同分层数下导体的温度值,求解导体温度随分层数的变化率,当变化率达到设定的变化率下限,此时分层数为最佳分层数。S5, importing each model parameter, using a loop statement, calculating the temperature value of the conductor under different layer numbers at a certain time, and solving the rate of change of the conductor temperature with the number of layers, when the rate of change reaches the lower limit of the set rate of change, at this time, layering The number is the optimal number of layers.
具体的:specific:
步骤1:选取某一时刻作为计算起点,导入此刻的导体温度、表皮温度、各层材料的热阻率和比热容等计算参数,进入下一步骤;Step 1: Select a certain moment as the starting point of calculation, and introduce the calculation parameters of the conductor temperature, the skin temperature, the thermal resistivity of each layer of material and the specific heat capacity at the moment, and proceed to the next step;
步骤2:设置分层数为1层,计算此时导体温度值T
11,进入下一步骤;
Step 2: Set the number of layers to 1 layer, calculate the conductor temperature value T 11 at this time, and proceed to the next step;
步骤3:设置分层数为2层,计算此时导体温度值T
12,较上一分层数计算温度随分层数的变化率,并取其绝对值|T
11-T
12|,若|T
11-T
12|小于设定值,则绝缘层的最佳分层数为2,结束,否则进入下一步骤;
Step 3: Set the number of layers to 2 layers, calculate the conductor temperature value T 12 at this time, calculate the rate of change of temperature with the number of layers compared with the previous layer, and take the absolute value |T 11 -T 12 |, if | T 11 -T 12 | is less than the set value, then the optimal number of layers of the insulating layer is 2, ending, otherwise it proceeds to the next step;
步骤4:取分层数变量i=3,进入下一步;Step 4: Take the layer number variable i=3 and proceed to the next step;
步骤5:设置分层数为i,计算此时导体温度值T
1i,较上一分层数计算温度随分层数的变化率,并取其绝对值|T
1(i-1)-T
1i|,若|T
1(i-1)-T
1i|小于设定值,则绝缘层的最佳分层数为i,结束,否则进入下一步骤;
Step 5: Set the number of layers to i, calculate the conductor temperature value T 1i at this time, calculate the rate of change of temperature with the number of layers compared with the previous layer, and take the absolute value |T 1(i-1) -T 1i |, if |T 1(i-1) -T 1i | is less than the set value, the optimal number of layers of the insulating layer is i, end, otherwise proceed to the next step;
步骤6:i=i+1,返回步骤5。Step 6: i=i+1, return to step 5.
S6、以S5中计算结果为基础,并重复S5中的步骤,确定下一时刻的绝缘层最佳分层数。S6. Based on the calculation result in S5, repeat the steps in S5 to determine the optimal number of layers of the insulation layer at the next moment.
以步骤S5确定最佳分层数下的导体温度计算结果作为下一时刻计算的导体温度导入值,再导入下一时刻的表皮温度值,其他导入的参数保持不变,重复步骤S5,得到下一时刻绝缘层的最佳分层数。In step S5, the conductor temperature calculation result under the optimal layer number is determined as the conductor temperature introduction value calculated at the next time, and then the skin temperature value at the next moment is imported, and the other imported parameters remain unchanged, and step S5 is repeated to obtain the next step. The optimal number of layers of insulation at a time.
S7、重复S5、S6,即可得到高压电缆暂态热路中绝缘层实时最佳分层数。S7, repeat S5, S6, the real-time optimal stratification number of the insulation layer in the transient hot path of the high-voltage cable can be obtained.
每下一时刻导体温度的计算均以上一时刻的计算结果为基础,不断重复步骤S5和步骤S6,即可得到整个温升过程中不同时刻绝缘层的最佳分层数,也就是实时、动态地确定高压电缆暂态热路中绝缘层最佳分层数。The calculation of the conductor temperature at each next moment is based on the calculation result at the previous moment. Repeating steps S5 and S6 are repeated to obtain the optimal number of layers of the insulation layer at different times during the entire temperature rise process, that is, real-time and dynamic. Determine the optimal number of layers of insulation in the transient thermal path of the high voltage cable.
上述实施例为本发明较佳的实施方式,但本发明的实施方式并不受上述实施例的限制,其他的任何未背离本发明的精神实质与原理下所作的改变、修饰、替代、组合、简化,均应为等效的置换方式,都包含在本发明的保护范围之内。The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and combinations thereof may be made without departing from the spirit and scope of the invention. Simplifications should all be equivalent replacements and are included in the scope of the present invention.
Claims (10)
- 一种动态确定高压电缆暂态热路中绝缘最佳分层数的方法,其特征在于,包括以下步骤:A method for dynamically determining the optimal number of layers of insulation in a transient thermal path of a high voltage cable, characterized in that it comprises the following steps:S1、选择所需高压电缆,确定其尺寸及各层材料物性参数;S1, selecting a required high-voltage cable, determining its size and physical property parameters of each layer;S2、构建电缆本体暂态热路模型及对应的数学模型,该步骤具体为:S2, constructing a cable body transient thermal path model and a corresponding mathematical model, the steps are specifically:S201、构建电缆本体暂态热路模型;S201, constructing a transient thermal path model of the cable body;S202、构建热路模型对应的数学模型;S202. Construct a mathematical model corresponding to the heat path model;S3、确定暂态热路模型中各参数,该步骤具体为:S3. Determine each parameter in the transient thermal path model, and the step is specifically:S301、时不变参数的确定;S301, determining the time-invariant parameter;S302、时变参数的确定;S302, determining a time-varying parameter;S4、根据步骤S2中的数学模型,采用MATLAB编辑计算程序;S4, according to the mathematical model in step S2, using MATLAB to edit the calculation program;S5、导入各模型参数,利用循环语句,计算某一时刻不同分层数下导体的温度值,求解导体温度随分层数的变化率,当变化率达到设定的变化率下限,此时分层数为最佳分层数;S5, importing each model parameter, using a loop statement, calculating the temperature value of the conductor under different layer numbers at a certain time, and solving the rate of change of the conductor temperature with the number of layers, when the rate of change reaches the lower limit of the set rate of change, at this time, layering The number is the optimal number of layers;S6、以S5中计算结果为基础,并重复S5中的步骤,确定下一时刻的绝缘层最佳分层数;S6, based on the calculation result in S5, and repeating the steps in S5 to determine the optimal number of layers of the insulation layer at the next moment;S7、重复S5、S6,即可得到高压电缆暂态热路中绝缘层实时最佳分层数。S7, repeat S5, S6, the real-time optimal stratification number of the insulation layer in the transient hot path of the high-voltage cable can be obtained.
- 根据权利要求1所述的动态确定高压电缆暂态热路中绝缘最佳分层数的方法,其特征在于,步骤S1中:根据计算需要,选择对象型号的高压电缆作为计算原型,确定相关电缆各层结构的参数包括:尺寸数据、材料特性、导热率、比热容、电阻率。The method for dynamically determining the optimal number of insulation layers in a transient thermal path of a high voltage cable according to claim 1, wherein in step S1: selecting a high voltage cable of the target model as a calculation prototype according to calculation requirements, and determining the relevant cable. The parameters of each layer structure include: size data, material properties, thermal conductivity, specific heat capacity, and electrical resistivity.
- 根据权利要求1所述的动态确定高压电缆暂态热路中绝缘最佳分层数的方法,其特征在于,所述步骤S201具体为:The method for dynamically determining the optimal number of layers in the transient thermal path of the high-voltage cable according to claim 1, wherein the step S201 is specifically:根据电缆线路和各层材料的特点,构建暂态热路模型基于以下假设:1)相对电缆半径,电缆线路长度无限大,对于长直电缆段,忽略其轴向传热;2)在一般敷设条件特别是实验条件下,电缆外部环境均匀,电缆各层材料各向同性,并且中心对称;3)各层材料的热容热阻不随时间空间而变化;4)内外屏蔽层很薄且热参数与绝缘层相似,因此三者合并同一层处理,5)相对导体损耗而言,介质损耗忽略不计,单端接地情况下忽略护套损耗;According to the characteristics of the cable line and the material of each layer, the transient thermal path model is based on the following assumptions: 1) the cable length is infinite relative to the cable radius, and the axial heat transfer is ignored for the long straight cable section; 2) in general laying Conditions, especially under experimental conditions, the external environment of the cable is uniform, the material of each layer of the cable is isotropic, and the center is symmetrical; 3) the heat capacity of each layer of material does not change with time space; 4) the inner and outer shielding layers are thin and thermal parameters Similar to the insulating layer, so the three are combined with the same layer of processing, 5) the dielectric loss is negligible in terms of relative conductor loss, and the sheath loss is ignored in the case of single-ended grounding;基于以上假设,电缆本体热路简化成沿着径向的一维热路模型,同时绝缘层采用等厚度 分层处理,电缆热路模型为分布参数暂态热路模型;设置:P表示电缆导体损耗;n-3表示绝缘层分层数;T 1表示电缆导体温度;T 2—T n-3表示电缆绝缘层,含内、外屏蔽各分层温度;T n-2表示绕包带温度;T n-1表示气隙层温度;T n表示铝护套温度;T o表示电缆表皮温度;C 1'表示电缆导体热容;C 1”、C 2—C n-3表示电缆绝缘层,含内、外屏蔽层各分层热容;C n-2表示绕包层热容;C n-1表示气隙层热容;C n'表示铝护套热容;C n”表示外护套热容;R 1—R n-3表示电缆绝缘层,含内、外屏蔽各分层热阻;R n-2表示绕包层热阻;R n-1表示气隙层热阻;R n表示外护套热阻。 Based on the above assumptions, the cable body thermal path is simplified into a one-dimensional heat path model along the radial direction, while the insulation layer is treated by equal thickness stratification, the cable thermal path model is a distributed parameter transient thermal path model; and the setting: P represents the cable conductor Loss; n-3 indicates the number of layers of the insulation layer; T 1 indicates the cable conductor temperature; T 2 -T n-3 indicates the cable insulation layer, including the inner and outer shield delamination temperatures; T n-2 indicates the winding temperature T n-1 represents the air gap layer temperature; T n represents the aluminum sheath temperature; T o represents the cable skin temperature; C 1 ' represents the cable conductor heat capacity; C 1 ”, C 2 — C n-3 represents the cable insulation layer Containing the heat capacity of each layer of the inner and outer shield layers; C n-2 means the heat capacity around the cladding; C n-1 means the heat capacity of the air gap layer; C n ' indicates the heat capacity of the aluminum sheath; C n ” means outside Sheath heat capacity; R 1 —R n-3 denotes the cable insulation layer, including the inner and outer shields of each layer of thermal resistance; R n-2 denotes the thermal resistance of the cladding layer; R n-1 denotes the thermal resistance of the air gap layer; R n represents the thermal resistance of the outer sheath.
- 根据权利要求3所述的动态确定高压电缆暂态热路中绝缘最佳分层数的方法,其特征在于,所述步骤S202具体为:The method for dynamically determining the optimal number of layers in the transient thermal path of the high-voltage cable according to claim 3, wherein the step S202 is specifically:对热路中的每个节点列写节点方程,并转化为矩阵表达形式:Write a node equation for each node in the heat path and convert it into a matrix representation:其中,C 1=C 1'+C 1”,C n=C n'+C n”,各矩阵如下: Where C 1 =C 1 '+C 1 ”, C n =C n '+C n ”, and the matrices are as follows:T=[T 1 T 2 T 3 L T n] T T=[T 1 T 2 T 3 L T n ] T
- 根据权利要求1所述的动态确定高压电缆暂态热路中绝缘最佳分层数的方法,其特征在于,所述步骤S301具体为:The method for dynamically determining the optimal number of layers in the transient thermal path of the high-voltage cable according to claim 1, wherein the step S301 is specifically:在暂态热路模型中,基于假设,时不变参数包括各层材料的热容、热阻,各层热容热阻以IEC 60287标准计算;In the transient thermal path model, based on the assumption, the time-invariant parameters include the heat capacity and thermal resistance of each layer of material, and the heat capacity of each layer is calculated according to the IEC 60287 standard;单位长度热容计算公式如下:The formula for calculating the heat capacity per unit length is as follows:式中:d 2为计算层外径;d 1为计算层内径;δ为计算层材料的体积热容; Where: d 2 is the calculated layer outer diameter; d 1 is the calculated layer inner diameter; δ is the calculated volumetric heat capacity of the layer material;单位长度热阻计算公式如下:The formula for calculating the thermal resistance per unit length is as follows:式中:d 1表示计算层内径;d 2表示计算层外径。 Where: d 1 represents the inner diameter of the calculation layer; d 2 represents the outer diameter of the calculation layer.
- 根据权利要求1所述的动态确定高压电缆暂态热路中绝缘最佳分层数的方法,其特征在于,所述步骤S302具体为:The method for dynamically determining the optimal number of layers in the transient hot path of the high-voltage cable according to claim 1, wherein the step S302 is specifically:在暂态热路模型中,时变参数包括导体损耗和电缆表面温度,其中电缆表面温度由热电偶实时测量所得,导体损耗随着导体电阻的变化而变化;In the transient thermal path model, the time-varying parameters include conductor loss and cable surface temperature, wherein the cable surface temperature is measured by the thermocouple in real time, and the conductor loss changes with the change of the conductor resistance;单位长度导体损耗计算如下:The conductor loss per unit length is calculated as follows:P=I 2r P=I 2 r式中:P为导体的发热功率;I为负荷电流;r为单位长度导体交流电阻;Where: P is the heating power of the conductor; I is the load current; r is the AC resistance per unit length of the conductor;导体工作温度下单位长度的交流电阻计算公式:Calculation formula of AC resistance per unit length at conductor operating temperature:r=r′(1+Y s+Y p) r=r'(1+Y s +Y p )式中:r为单位长度导体的交流电阻;r′为单位长度导体的直流电阻;Y s为集肤效应因数;Y p为邻近效应因数; Where: r is the alternating current resistance of the conductor of unit length; r' is the direct current resistance of the conductor of unit length; Y s is the skin effect factor; Y p is the adjacent effect factor;单位长度导体的直流电阻计算公式:The formula for calculating the DC resistance of a conductor per unit length:r′=r 0×[1+α(θ-20)] r'=r 0 ×[1+α(θ-20)]式中:r 0为20℃时单位长度电缆导体的直流电阻;α为导体的电阻温度系数;θ为工作温度; Where: r 0 is the DC resistance of the cable conductor per unit length at 20 ° C; α is the temperature coefficient of resistance of the conductor; θ is the operating temperature;集肤效应因数Y s计算公式: Skin effect factor Y s calculation formula:式中:k s为经验值;f为电流频率。 Where: k s is the empirical value; f is the current frequency.
- 根据权利要求4所述的动态确定高压电缆暂态热路中绝缘最佳分层数的方法,其特征在于,所述步骤S4具体为:The method for dynamically determining the optimal number of layers in the transient hot path of the high-voltage cable according to claim 4, wherein the step S4 is specifically:根据系列节点所列方程组以及其中各参数的计算方法,采用MATLAB软件,编辑矩阵A、B、P的计算程序和微分方程组的求解程序。According to the equations listed in the series of nodes and the calculation methods of each parameter, the calculation program of matrix A, B, P and the solution program of differential equations are edited by MATLAB software.
- 根据权利要求1所述的动态确定高压电缆暂态热路中绝缘最佳分层数的方法,其特征在于,所述步骤S5具体为:The method for dynamically determining the optimal number of layers of insulation in the transient thermal path of the high-voltage cable according to claim 1, wherein the step S5 is specifically:步骤1:选取某一时刻作为计算起点,导入此刻的计算参数,进入下一步骤;Step 1: Select a certain moment as the starting point of calculation, import the calculation parameters at the moment, and proceed to the next step;步骤2:设置分层数为1层,计算此时导体温度值T 11,进入下一步骤; Step 2: Set the number of layers to 1 layer, calculate the conductor temperature value T 11 at this time, and proceed to the next step;步骤3:设置分层数为2层,计算此时导体温度值T 12,较上一分层数计算温度随分层数的变化率,并取其绝对值|T 11-T 12|,若|T 11-T 12|小于设定值,则绝缘层的最佳分层数为2,结束,否则进入下一步骤; Step 3: Set the number of layers to 2 layers, calculate the conductor temperature value T 12 at this time, calculate the rate of change of temperature with the number of layers compared with the previous layer, and take the absolute value |T 11 -T 12 |, if | T 11 -T 12 | is less than the set value, then the optimal number of layers of the insulating layer is 2, ending, otherwise it proceeds to the next step;步骤4:取分层数变量i=3,进入下一步;Step 4: Take the layer number variable i=3 and proceed to the next step;步骤5:设置分层数为i,计算此时导体温度值T 1i,较上一分层数计算温度随分层数的变化率,并取其绝对值|T 1(i-1)-T 1i|,若|T 1(i-1)-T 1i|小于设定值,则绝缘层的最佳分层数为i,结束,否则进入下一步骤; Step 5: Set the number of layers to i, calculate the conductor temperature value T 1i at this time, calculate the rate of change of temperature with the number of layers compared with the previous layer, and take the absolute value |T 1(i-1) -T 1i |, if |T 1(i-1) -T 1i | is less than the set value, the optimal number of layers of the insulating layer is i, end, otherwise proceed to the next step;步骤6:i=i+1,返回步骤5。Step 6: i=i+1, return to step 5.
- 根据权利要求8所述的动态确定高压电缆暂态热路中绝缘最佳分层数的方法,其特征在于,所述步骤S6具体为:The method for dynamically determining the optimal number of layers in the transient thermal path of the high-voltage cable according to claim 8, wherein the step S6 is specifically:以权利要求8确定最佳分层数下的导体温度计算结果作为下一时刻计算的导体温度导入值,再导入下一时刻的表皮温度值,其他导入的参数保持不变,重复权利要求8中各步骤,得到下一时刻绝缘层的最佳分层数。Determine the conductor temperature calculation result under the optimal layer number according to claim 8 as the conductor temperature introduction value calculated at the next time, and then import the skin temperature value at the next moment, and the other imported parameters remain unchanged, repeating the claim 8 In each step, the optimal number of layers of the insulating layer at the next moment is obtained.
- 根据权利要求9所述的动态确定高压电缆暂态热路中绝缘最佳分层数的方法,其特征在于,所述步骤S7具体为:The method for dynamically determining the optimal number of layers in the transient thermal path of the high-voltage cable according to claim 9, wherein the step S7 is specifically:每下一时刻导体温度的计算均以上一时刻的计算结果为基础,不断重复权利要求8和9中各步骤,即可得到整个温升过程中不同时刻绝缘层的最佳分层数,也就是实时确定高压电缆暂态热路中绝缘层最佳分层数。The calculation of the conductor temperature at each next moment is based on the calculation result at the previous moment, and the steps in claims 8 and 9 are continuously repeated to obtain the optimum number of layers of the insulating layer at different times during the entire temperature rise process, that is, The optimal number of layers of the insulation layer in the transient thermal path of the high voltage cable is determined in real time.
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