A cable joint treeing prediction method based on parallel markov chain

Abstract

The application discloses a cable joint electric tree prediction method based on parallel Markov chains and belongs to the electric tree prediction field. The cable joint electric tree prediction method based on parallel Markov chains comprises the following steps: establishing a cable joint model; defining cable parameters; calculating the numerical distribution of electric fields and thermal fields in cross-linked polyethylene and silicone rubber materials of a distribution network cable joint; judging the cross-linked polyethylene internal electric tree development condition according to the electric field intensity; calculating the electric tree bifurcation probability density function according to the electric field intensity in each direction and the parallel Markov chain theory, revealing the electric tree bifurcation mechanism and calculating the bifurcation electric tree conductivity; taking the electric tree energy as a criterion to study the specific process of electric tree development or stop; through iterative calculation, simulating the random process of the development of the electric tree in the cross-linked polyethylene material, forming the electric tree distribution, repeatedly performing the process multiple times, inferring the characteristics of the electric tree distribution, and obtaining the relevance law of the electric tree bifurcation mechanism and the final shape of the electric tree.

Description

Technical Field

[0001] This invention relates to the field of electrical tree prediction, and more specifically to a method for predicting electrical trees in cable joints based on parallel Markov chains. Background Technology

[0002] Cable joints connect cables and extend power transmission. Electrical treeing is a typical degradation phenomenon that leads to cable joint breakdown accidents. Therefore, the study of electrical treeing is helpful for the design and installation of 10kV XLPE cables. However, existing algorithms or models are difficult to apply to the prediction of electrical tree trajectories. For example, traditional Markov chains have difficulty modeling branching phenomena and creating multiple trajectories simultaneously. Summary of the Invention

[0003] Based on the aforementioned technical problems, this invention constructs a parallel Markov chain to simulate the development paths of multiple branches of various types of electrical branches, while simultaneously recording the development trends of multiple paths.

[0004] The objective of this invention can be achieved through the following technical solutions:

[0005] A method for predicting the electrical tree of cable joints based on parallel Markov chains includes the following steps:

[0006] S1: Establish a cable joint model;

[0007] S2: Specifies cable parameters;

[0008] S3: Calculate the numerical distribution of electric and thermal fields in the cross-linked polyethylene and silicone rubber materials of the cable joint;

[0009] S4: Determine the conditions for the development of electrical trees inside cross-linked polyethylene based on the magnitude of the electric field strength;

[0010] S5: Calculate the probability density function of electric tree bifurcation based on the electric field intensity in each direction and the parallel Markov chain theory, reveal the electric tree bifurcation mechanism, and calculate the conductivity of the bifurcation electric tree.

[0011] S6: Using the energy of the electric tree as a criterion, study the specific process of the development or cessation of the electric tree;

[0012] S7: Through iterative calculation, the random process of electrical tree development in cross-linked polyethylene material is simulated to form electrical tree distribution. The process is repeated multiple times to infer the characteristics of electrical tree distribution and obtain the correlation law between electrical tree bifurcation mechanism and final shape of electrical tree.

[0013] Optionally, in step S3, the method for calculating the electric field in the cross-linked polyethylene and silicone rubber materials of the distribution network cable joint includes the following steps:

[0014] The electric potential is calculated, and the potential distribution conforms to the Poisson equation:

[0015]

[0016] In the formula, It is the electric potential;

[0017] The electric field strength E can be obtained from the electric potential φ:

[0018]

[0019]

[0020] In the formula, and It is a unit vector along the positive directions of the X, Y, and Z axes.

[0021] Optionally, in step S3, the method for calculating the thermal field in the cross-linked polyethylene and silicone rubber materials of the distribution network cable joint includes the following steps:

[0022]

[0023] In the formula, T is the thermodynamic temperature at the point, t is time, ρ, c and λ are the density, specific heat capacity and thermal conductivity of the material at the point, respectively, and Φ is the heat source in the field.

[0024] Optionally, the heat transfer coefficient α at the interface between the insulating material and the electrical tree is calculated as follows:

[0025]

[0026] The heat transfer energy caused by conduction and convection is calculated as follows:

[0027]

[0028] In the formula, W heat It is the heat transfer energy, T(t) is the temperature of the electric tree, T i These are air temperature and insulating material, respectively, where α is the thermal conductivity of the insulating material, and S(l i (t) is the heat transfer region as a function of time and electric tree length, l i The length of the electric tree is represented by t0, which is the time from the start of heat transfer to the calculation time.

[0029] Optionally, in step S5, the probability density of electrical tree branching is calculated by the following formula:

[0030]

[0031] In the formula, n is the number of possible directions the electrical tree can develop, P(i) is the probability that the electrical tree will develop in the i-th direction, and E i E is the magnitude of the electric field intensity along the i-th direction. cM is the breakdown field strength of the air, M is the current position of the electrical tree, and W is the grounding field strength of the air. M Wc is the critical energy value of the multi-branch electric tree; τ(x) is a step function.

[0032]

[0033] The energy balance expression during tree development is:

[0034] αC0πεE 2 +FdΔ=gdL+gsdL (8)

[0035] In the formula: E represents the local electric field strength; ε represents the dielectric constant, so Ge≡πεE2 can be used to represent the energy released when the void increases in length per unit length; αC0 represents the volume of the local electric field activation region, and α is related to the type of material; F represents the applied force; Δ represents the displacement; L represents the length of the electric tree channel; g represents the energy required to overcome surface energy and material deformation when the electric tree grows forward by a unit length; gs represents the energy dissipated by the energy stored in the potential damage region when the electric tree grows forward by a unit length.

[0036] Alternatively, the driving force for the development of the electrical tree is provided by VdQ+Fdα, using It means that when At this time, the electric tree cannot grow forward, but it can continue to grow if it moves backward;

[0037] The probability density of branching of the electrical tree can be calculated by the following formula:

[0038]

[0039] In the formula, n is the number of possible directions the electrical tree can develop, P(i) is the probability that the electrical tree will develop in the i-th direction, and E i E is the magnitude of the electric field intensity along the i-th direction. c M is the breakdown field strength of the air, and M is the current position of the electrical tree; W M It is the critical energy value of the multi-branch electric tree, W c It is the critical value of the multi-branch energy of the electric tree.

[0040] A computer-readable storage medium storing instructions that, when executed, enable the implementation of any of the above-described electrical tree prediction methods.

[0041] The beneficial effects of this invention are:

[0042] Traditional Markov chains struggle to model branching phenomena and simultaneously create multiple trajectories. Therefore, PMC (Power Tree Management) was developed to simulate the development paths of multiple branches in various types of electrical branches, while simultaneously recording the development trends of multiple trajectories. This invention chooses to describe electrical tree growth using parallel Markov chains. The electrical tree energy consists of the energy absorbed and dissipated during the tree's propagation. The traditional process is optimized by implementing fractal criteria and energy transfer to branching and suppressing tree growth. The variance of the electric field strength is used as a reference to determine the development conditions of the next state. This design reflects both the development trajectory of the electrical tree under the influence of an electro-thermal coupling field and the randomness of its development. Electrical treeing is a typical degradation phenomenon leading to cable joint breakdown accidents; therefore, the research on electrical tree mechanisms in this invention helps extend the service life of 10kV XLPE cables.

[0043] Meanwhile, based on the calculation of the numerical distribution of the electric field and the numerical distribution of the thermal field, this invention calculates the probability density function of electric tree bifurcation according to the parallel Markov chain theory. Therefore, the specific process of electric tree development or cessation can be studied using electric tree energy as a criterion, and the stochastic process of electric tree development in cross-linked polyethylene materials can be simulated, which can be used for the prediction and analysis of electric tree trajectory. Attached Figure Description

[0044] The invention will now be further described with reference to the accompanying drawings.

[0045] Figure 1 This is a schematic diagram of the process of the present invention;

[0046] Figure 2 Schematic diagram of tree-like and cluster-like electrical trees;

[0047] Figure 3 This is a cross-section of an XLPE cable.

[0048] Figure 4 This is the Markov chain used in this application. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] In some examples of this invention, a method for predicting the electrical tree of a cable joint based on a parallel Markov chain is disclosed, comprising the following steps:

[0051] S1: Determine parameters such as cable joint size and cable core voltage rating;

[0052] After establishing the distribution network cable joint model, it is necessary to determine parameters such as cable joint dimensions and cable core voltage level, including the heat transfer coefficient αi at the electrical tree interface and the potential of the high-voltage electrode. And boundary conditions, as well as the relevant dimensions given according to the specific shape of the cable joint.

[0053] S2: Calculate the numerical distribution of electric and thermal fields in cross-linked polyethylene and silicone rubber materials of distribution network cable joints;

[0054] The electric and thermal fields in the cable joint are determined by the wide-area time-domain finite-difference method. Figure 2 In the structural calculations, the potential distribution conforms to the Poisson equation:

[0055]

[0056] In the formula, It represents the electric potential.

[0057] The magnitude of the electric field strength E can be determined by the electric potential. Find:

[0058]

[0059] The temperature distribution conforms to the heat conduction differential equation:

[0060]

[0061] In the formula, T is the thermodynamic temperature at the point, t is time, ρ, c and λ are the density, specific heat capacity and thermal conductivity of the material at the point, respectively, and Φ is the heat source in the field (the surface of the insulator and the electric tree can both be used as heat sources).

[0062] S3: Determine the conditions for the development of electrical trees inside cross-linked polyethylene based on the magnitude of the electric field strength;

[0063] If the magnitude of the electric field strength at a point P within the electric field region is E P The initial electric field strength E, which is greater than or equal to the electric field strength E that appears inside the cross-linked polyethylene, is also present. c If so, then an electric tree may appear at that point.

[0064] S4: Calculate the probability density function of electric tree branching based on the electric field strength in each direction and the parallel Markov chain theory;

[0065] The probability density function of electric tree branching can be calculated by the following formula:

[0066]

[0067] In the formula, n is the number of possible directions the electrical tree can develop, P(i) is the probability that the electrical tree will develop in the i-th direction, and E i It represents the magnitude of the electric field intensity along the i-th direction. τ(x) is a step function:

[0068]

[0069] S5: Using the energy of the electric tree as a criterion, study the specific process of the development or cessation of the electric tree;

[0070] The generated random number rand takes values ​​from 0 to 1, that is...

[0071] 0≤rand≤1 (6)

[0072] For the i-th development direction, if rand falls within this range (if i = 1, then the "<" on the left side of rand is changed to "≤"):

[0073]

[0074] and

[0075] E i ≥E c (8)

[0076] Then the electric tree develops in the i-th direction.

[0077] if

[0078] E i <E c (9)

[0079] The electric tree will temporarily stop growing in any direction.

[0080] S6: Calculate the energy injected and dissipated by the electrical tree;

[0081] The energy of an electric tree consists of the energy absorbed and dissipated during its development. The calculation method for electric tree energy is as follows:

[0082] W tree =W injection -W dissipation (10)

[0083]

[0084] In the formula, i leakage (x,t) represents the leakage current on the electric tree at any time during the propagation process, t0 is the time from the start of the electric tree to the calculation time, and l is the length of the electric tree.

[0085] W dissipation =gdL+g s dL (12)

[0086] In the formula, g represents the energy required to overcome surface energy and material deformation per unit length of forward growth of the electric tree; g sThis represents the energy dissipated when the electric tree grows a unit length forward, the energy stored in the potential damage zone.

[0087] The driving force behind the development of electric trees is W injection Provide, use It means that when At this time, the electric tree cannot grow forward, but it can continue to grow. It is not a constant; it is related to a variety of factors such as electrode shape, applied voltage, and frequency.

[0088] Due to charge injection, some areas with weak insulation properties are formed in the region, which then causes the material molecular chains to break. As the broken chains accumulate, voids are formed. The strong electric field around the voids leads to more and more voids. Multiple voids connect to form macroscopic electric tree channel branches.

[0089] Heat transfer and convection are the main forms of heat transfer between electric trees. The partial differential equation (PDE) for heat conduction and the boundary conditions are given as follows:

[0090]

[0091] In the formula, T is the thermal temperature, t is the time, ρ, c and λ represent the density, specific heat capacity and thermal conductivity of different insulating materials, respectively, and Φ is the internal heat source caused by the leakage current density in the electrical tree and silicone rubber or XLPE material.

[0092] Thermal convection is the heat transfer process involving the relative motion between the electrical tree and the insulating medium. The convective motion between the electrical tree and the insulating medium is represented by the mass and momentum protection equations as follows:

[0093]

[0094] In the formula, ρ is the fluid density, p is the pressure, u, v and w are the x, y and z components of the fluid velocity, respectively, and η is the viscous stressor.

[0095] S7: Through iterative calculations, the stochastic process of electrical tree development in cross-linked polyethylene materials can be simulated, forming different electrical tree distributions such as clusters and forks. Repeating this process multiple times can infer the characteristics of the electrical tree trajectory distribution.

[0096] PMC optimizes the traditional process by implementing fractal criteria and transferring energy to branching and inhibiting tree growth, using the variance of the electric field strength as a reference to determine whether the next state is growth, branching, or cessation. After the calculation process, a random trajectory of one type of electric tree can be obtained. Repeating steps S1 to S7 multiple times yields a series of electric tree development trajectories, thereby inferring the characteristics of the electric tree trajectory distribution.

[0097] In other examples of the invention, a computer-readable storage medium storing instructions is also involved. When executed, the instructions enable the cable joint electrical tree prediction method based on parallel Markov chains described in the above examples. More specifically, the instructions may be a computer-readable language. The computer described above can be a general-purpose computer device or a special-purpose computer device. In specific implementations, the computer may be a desktop computer, a portable computer, a network server, a PDA (Personal Digital Assistant), a mobile phone, a tablet computer, a wireless terminal device, a communication device, or an embedded device. The storage medium may be any available medium accessible to the computer or a data storage device such as a server or data center that integrates one or more available media. For example, the storage medium may be, but is not limited to, magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., Digital Versatile Discs (DVDs)), or semiconductor media (e.g., solid-state drives (SSDs)).

[0098] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0099] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A method for predicting the electrical tree of cable joints based on parallel Markov chains, characterized in that, Includes the following steps: S1: Establish a cable joint model; S2: Specifies cable parameters; S3: Calculate the numerical distribution of electric and thermal fields in the cross-linked polyethylene and silicone rubber materials of the cable joint; S4: Determine the conditions for the development of electrical trees inside cross-linked polyethylene based on the magnitude of the electric field strength; S5: Calculate the probability density function of electric tree bifurcation based on the electric field intensity in each direction and the parallel Markov chain theory, reveal the electric tree bifurcation mechanism, and calculate the conductivity of the bifurcation electric tree. S6: Using the energy of the electric tree as a criterion, study the specific process of the development or cessation of the electric tree; S7: Through iterative calculation, the random process of electrical tree development in cross-linked polyethylene material is simulated to form electrical tree distribution. The process is repeated multiple times to infer the characteristics of electrical tree distribution and obtain the correlation law between electrical tree bifurcation mechanism and final shape of electrical tree.

2. The cable joint electrical tree prediction method based on parallel Markov chains according to claim 1, characterized in that, In step S3, the method for calculating the electric field in the cross-linked polyethylene and silicone rubber materials of the distribution network cable joint includes the following steps: The electric potential is calculated, and the potential distribution conforms to the Poisson equation: In the formula, It is the electric potential; The electric field strength E can be obtained from the electric potential φ: In the formula, and It is a unit vector along the positive directions of the X, Y, and Z axes.

3. The cable joint electrical tree prediction method based on parallel Markov chains according to claim 1, characterized in that, In step S3, the method for calculating the thermal field in the cross-linked polyethylene and silicone rubber materials of the distribution network cable joint includes the following steps: In the formula, T is the thermodynamic temperature at the point, t is time, ρ, c and λ are the density, specific heat capacity and thermal conductivity of the material at the point, respectively, and Φ is the heat source in the field.

4. The cable joint electrical tree prediction method based on parallel Markov chains according to claim 1, characterized in that, The heat transfer coefficient α at the interface between the insulating material and the electrical tree is calculated as follows: The heat transfer energy caused by conduction and convection is calculated as follows: In the formula, W heat It is the heat transfer energy, T(t) is the temperature of the electric tree, T i These are air temperature and insulating material, respectively, where α is the thermal conductivity of the insulating material, and S(l i (t) is the heat transfer region as a function of time and electric tree length, l i The length of the electric tree is represented by t0, which is the time from the start of heat transfer to the calculation time.

5. The cable joint electrical tree prediction method based on parallel Markov chains according to claim 1, characterized in that, In step S5, the probability density of electrical tree branching is calculated by the following formula: In the formula, n is the number of possible directions the electrical tree can develop, P(i) is the probability that the electrical tree will develop in the i-th direction, and E i E is the magnitude of the electric field intensity along the i-th direction. c M is the breakdown field strength of the air, M is the current position of the electrical tree, and W is the grounding field strength of the air. M Wc is the critical energy value of the multi-branch electric tree; τ(x) is a step function. The energy balance expression during tree development is: αC0πεE 2 +FdΔ=gdL+gsdL (8) In the formula: E represents the local electric field strength; ε represents the dielectric constant, so Ge≡πεE2 can be used to represent the energy released when the void increases in length per unit length; αC0 represents the volume of the local electric field activated region, and α is related to the type of material; F represents the applied force. Δ represents displacement; L represents the length of the electrical tree channel; g represents the energy required to overcome surface energy and material deformation per unit length of electrical tree propagation; gs represents the energy dissipated from the energy stored in the potential damage zone per unit length of electrical tree propagation.

6. The cable joint electrical tree prediction method based on parallel Markov chains according to claim 1, characterized in that, The driving force for the development of the electric tree is provided by VdQ+FdΔ, using g t c It means that when g t c <g+g s At this time, the electric tree cannot grow forward, but it can continue to grow if it moves backward; The probability density of branching of the electrical tree can be calculated by the following formula: In the formula, n is the number of possible directions the electrical tree can develop, P(i) is the probability that the electrical tree will develop in the i-th direction, and E i E is the magnitude of the electric field intensity along the i-th direction. c It is the breakdown field strength of the air, and M is the current position of the electric tree; W M It is the critical energy value of the multi-branch electric tree, W c It is the critical value of the multi-branch energy of the electric tree.

7. A computer-readable storage medium storing instructions that, when executed, enable the electrical tree prediction method according to any one of claims 1 to 6.

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