Precise submarine cable transmission line analytical model construction method based on IWOA algorithm

Abstract

A precise submarine cable transmission line analytical model building method based on an IWOA algorithm comprises a model building step, a parameter solving step and a parameter optimizing step, in the parameter optimizing step, a submarine cable whole-layer armoring finite element model is built based on a finite element method by referring to a simplified structure of a submarine cable, and through MATLAB and COMSOL joint simulation, the whole-layer armoring finite element model of the submarine cable is built; and searching the resistivity and magnetic conductivity of the submarine cable armor layer based on an IWOA algorithm to obtain a search result close to a reference value, and applying the optimized resistivity and magnetic conductivity to a transmission line analytical calculation model of the submarine cable. The method has the beneficial effects that compared with an unoptimized transmission line model, the optimized transmission line model has a more accurate simulation result.

Description

Technical Field

[0001] The present invention relates to the field of power cables, and in particular to a method for constructing an accurate submarine cable transmission line analytical model based on an IWOA algorithm. Background Art

[0002] In recent years, with the continuous expansion of energy demand in coastal areas, offshore wind power generation has developed rapidly around the world. AC transmission is an important form of offshore power transmission. Usually, offshore wind power within 50km adopts AC transmission. In order to improve the power transmission efficiency, it is necessary to increase the AC voltage level. Submarine cables above 110kV are generally single-core structures. Since the submarine cable needs to be grounded at both ends, induced circulation will appear in the grounding loop. Analysis of the circulation in the single-core submarine cable is of great significance for optimizing the submarine cable design and analyzing the system loss. It is an important basis for ensuring offshore energy security. Analytical calculation based on the transmission line model is a classic method for studying submarine cable circulation, but the current method generally believes that the submarine cable armor layer is a uniform whole layer structure when modeling, which is different from the metal wire (steel wire) armor of the actual submarine cable. This difference will lead to calculation errors. Summary of the invention

[0003] The purpose of the present invention is to solve the above problems and design a method for constructing an accurate submarine cable transmission line analytical model based on the IWOA algorithm. The specific design scheme is:

[0004] A method for constructing an accurate submarine cable transmission line analytical model based on an IWOA algorithm comprises a model building step, a parameter obtaining step and a parameter optimization step. In the model building step, based on the transmission line theory, an analytical calculation model of the transmission line of a submarine cable is established in MATLAB. In the parameter obtaining step, a finite element model of a submarine cable steel wire armor is established based on a finite element method, and the induced voltage and ground loop current of the sheath and the armor are calculated as reference values ​​for model optimization. In the parameter optimization step, a finite element model of the entire armor layer of the submarine cable is established based on the finite element method with reference to the simplified structure of the submarine cable. Through joint simulation with MATLAB and COMSOL, and based on the IWOA algorithm, the resistivity and permeability of the submarine cable armor layer are searched to obtain a search result close to the reference value, and the optimized resistivity and permeability are used in the analytical calculation model of the submarine cable transmission line to improve the simulation efficiency.

[0005] In the model building step, the transmission line modeling formula of the cable is as follows. The voltage and current waves of the conductor at the z position along the cable axis in the transmission line model are calculated by the telegraph equation (1):

[0006]

[0007]

[0008] V and I are defined as:

[0009] V=(V c , V s , V a ) T

[0010] I=(I c , I s , I a ) T (2)

[0011] Among them, V c , V s , V a is the voltage of the conductor, metal sheath and armor relative to the ground. The subscripts of the current I follow the same meaning. The impedance matrix Z and the admittance matrix Y are defined as follows:

[0012]

[0013] For submarine cables, the common ground is the reference voltage for multi-conductor transmission line analysis. The impedance and admittance between each metal layer of the cable are as follows: Figure 3 shown.

[0014] The elements in the impedance matrix Z are calculated as follows:

[0015] Z cc =z c，out +z ins，1 z s，in -2z s，m +z s，out +z ins，2 +z a，in -2z a，m +z a，out +z ins，3 +z g

[0016] Z cs =-z sm +z s，out +z ins，2 +z a，in -2z a，m +z a，out +z ins，3 +z g

[0017] z ss =z s，out +z ins，2 +z a，in -2z a，m +z a，out +z ins，3 +z g

[0018] Z ca =Z sa =-z a，m +z a，out +z ins，3 +z g

[0019] Z aa =z a，out +z ins，3 +z g (4)

[0020] Among them, z c，out is the internal impedance of the conductor, z ins，1 is the impedance caused by the time-varying magnetic field in the XLPE insulation, z s，in is the internal impedance of the inner sheath, z s，m is the sheath mutual impedance, z s，out is the internal impedance of the outer surface of the sheath, z ins，2 is the impedance caused by the time-varying magnetic field in the insulation between the lead sheath and the armor, z ins，3 is the impedance caused by the time-varying magnetic field in the outer sheath, z g is the self-impedance of the ground loop.

[0021] The transmission line analytical calculation method assumes that the submarine cable armor layer is a uniform whole layer structure when modeling the submarine cable, which is different from the metal wire armor structure of the actual submarine cable. It is necessary to optimize the parameters of the armor layer in the transmission line submarine cable model, where the associated impedance parameter of the armor layer is z a，in , z a，m and z a，out .z a，in is the internal impedance of the armor (the voltage drop on the inner surface of the sheath per unit current returned through the conductor)

[0022]

[0023]

[0024] ρ a , μ a and m a They are the resistivity, magnetic permeability and reverse penetration depth of the armor respectively.

[0025] z a，m It is the mutual impedance of the sheath, which indicates the voltage drop along the outer (inner) surface of the sheath when the unit current returns through the inner (outer) conductor. Here, the outer conductor is grounded.

[0026]

[0027] z a，out is the internal impedance of the outer surface of the armor (the voltage drop along the outer surface of the sheath when the current returns through the ground)

[0028]

[0029] The Y matrix can be expressed by the following formula

[0030]

[0031]

[0032]

[0033] Y cs =-Y oc Y ca =0

[0034]

[0035] Among them, ε XLPE is the relative dielectric constant of XLPE, ε bedding is the relative dielectric constant of the armor cushion layer, ε outersheath is the relative dielectric constant of the outer sheath.

[0036] In the parameter obtaining step, a finite element model of an armored steel wire submarine cable is established, and the control equation to be solved is as follows:

[0037]

[0038] Where: is the vector differential operator; H is the magnetic field intensity (A / m); J (A / m 2 ) is the current density vector; B is the magnetic induction intensity (T); A is the magnetic vector (wb / m); σ (S / m) is the conductivity; E (V / m) is the electric field vector; J e (A / m 2 ) is the external injection current density. The voltage value can be obtained by integrating the field strength E in the formula.

[0039] A simplified alternative model of the submarine cable was built to measure the induced voltage of the sheath and armor. The simulation results of the finite element submarine cable model were compared with the experimental results to verify the correctness of the finite element model. The induced voltage and ground loop current of the sheath and armor were taken as reference values.

[0040] In the parameter optimization step, establish Figure 2 The finite element model of the whole armored submarine cable shown in the figure sets the magnetic permeability and resistivity of the armor layer as independent variables, the induced voltage and ground loop current of the submarine cable sheath and armor as dependent variables, and the induced voltage and ground loop current in the simulation results of the armored steel wire submarine cable finite element model as target values. The error function is set as

[0041]

[0042]

[0043] Where f1 is the error function of the induced voltage, V 整层 and is the effective value and phase of the induced voltage in the whole armored submarine cable model, V 钢丝 and is the effective value and phase of the induced voltage in the steel wire armored submarine cable model; f2 is the error function of the ground loop current, I 整层 and is the effective value and phase of the ground loop current in the whole armored submarine cable model, I 钢丝 and is the effective value and phase of the ground loop current in the steel wire armored submarine cable model.

[0044] The resistivity and permeability of the armor in the whole-layer armored submarine cable model are optimized by the IWOA algorithm to obtain calculation results close to the reference values. The equivalent armor resistivity and permeability are extracted and brought into the analytical calculation model of the submarine cable transmission line to improve the simulation accuracy.

[0045] The accurate submarine cable transmission line analytical model construction method based on the IWOA algorithm obtained by the above technical solution of the present invention has the following beneficial effects:

[0046] Firstly, the analytical calculation model of submarine cable transmission line is established through transmission line theory, and then the finite element simulation model and MATLAB joint simulation are used to obtain the equivalent optimized resistivity and permeability of the whole armor structure of the submarine cable through the IWOA algorithm, and used in the analytical calculation model of submarine cable transmission line. Compared with the analytical calculation model of submarine cable transmission line without equivalent, the equivalent result has higher simulation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is the detailed cable structure of the present invention;

[0048] Figure 2 It is the simplified cable structure of the present invention;

[0049] Figure 3 is the cross-sectional relationship of the submarine cable described in the present invention;

[0050] Figure 4 It is a flow chart of parameter optimization of the whole-layer armored submarine cable according to the present invention;

[0051] Figure 5 It is a flowchart of the IWOA algorithm submarine cable parameter optimization of the present invention;

[0052] Figure 6 are the material parameters of the 220kV power cable described in the present invention;

[0053] Figure 7 It is a comparison of simulation results before and after the resistivity and permeability are equivalent as described in the present invention. DETAILED DESCRIPTION

[0054] The present invention will be described below in conjunction with the accompanying drawings.

[0055] A method for constructing an accurate analytical model of a submarine cable transmission line based on an IWOA algorithm comprises a model building step, a parameter obtaining step and a parameter optimization step. In the model building step, based on the transmission line theory, a transmission line analytical calculation model of a submarine cable is established by MATLAB. In the parameter obtaining step, a finite element model of a submarine cable steel wire armor is established based on a finite element method, and the induced voltage and ground loop current of a sheath and armor are calculated as reference values ​​for model optimization. In the parameter optimization step, a finite element model of the entire armor layer of the submarine cable is established based on the finite element method with reference to a simplified structure of the submarine cable. Through joint simulation of MATLAB and COMSOL, the resistivity and permeability of the submarine cable armor layer are searched based on the IWOA algorithm to obtain a search result close to the reference value, and the optimized resistivity and permeability are used in the analytical calculation model of the transmission line of the submarine cable to improve the simulation efficiency.

[0056] In the model building step, the transmission line modeling formula of the cable is as follows. The voltage and current waves of the conductor at the z position along the cable axis in the transmission line model are calculated by the telegraph equation (1):

[0057]

[0058]

[0059] V and I are defined as:

[0060] V=(V c , V s , V a ) T

[0061] I=(I c , I s , I a ) T (2)

[0062] Among them, V c , V s , V a is the voltage of the conductor, metal sheath and armor relative to the ground. The subscripts of the current I follow the same meaning. The impedance matrix Z and the admittance matrix Y are defined as follows:

[0063]

[0064] For submarine cables, the common ground is the reference voltage for multi-conductor transmission line analysis. The impedance and admittance between each metal layer of the cable are as follows: Figure 3 shown.

[0065] The elements in the impedance matrix Z are calculated as follows:

[0066] Z cc =z c，out +z ins，1 +z s，in -2z s，m +z s，out +z ins，2 +z a，in -2z a，m +z a，out +z ins，3 +z g

[0067] Z cs =-z sm +z s，out +z ins，2 +z a，in -2z a，m +z a，out +z ins，3 +z g

[0068] Z ss =z s，out +z ins，2 +z a，in -2z a，m +z a，out +z ins，3 +z g

[0069] Z ca =Z sa =-z a，m +z a，out +z ins，3 +z g

[0070] Z aa =z a，out +z ins，3 +z g (4)

[0071] Among them, z c，out is the internal impedance of the conductor, z ins，1 is the impedance caused by the time-varying magnetic field in the XLPE insulation, z s，in is the internal impedance of the inner sheath, z s，m is the sheath mutual impedance, z s，out is the internal impedance of the outer surface of the sheath, z ins，2is the impedance caused by the time-varying magnetic field in the insulation between the lead sheath and the armor, z ins，3 is the impedance caused by the time-varying magnetic field in the outer sheath, z g is the self-impedance of the ground loop.

[0072] The transmission line analytical calculation method assumes that the submarine cable armor layer is a uniform layer structure when modeling the submarine cable, which is different from the metal wire armor structure of the actual submarine cable. This patent optimizes the parameters of the armor layer in the transmission line submarine cable model, where the associated impedance parameter of the armor layer is z a，in , z a，m and z a，out .z a，in is the internal impedance of the armor (the voltage drop on the inner surface of the sheath per unit current returned through the conductor)

[0073]

[0074]

[0075] ρ a , μ a and m a They are the resistivity, magnetic permeability and reverse penetration depth of the armor respectively.

[0076] z a，m It is the mutual impedance of the sheath, which indicates the voltage drop along the outer (inner) surface of the sheath when the unit current returns through the inner (outer) conductor. Here, the outer conductor is grounded.

[0077]

[0078] z a，out is the internal impedance of the outer surface of the armor (the voltage drop along the outer surface of the sheath when the current returns through the ground)

[0079]

[0080] The Y matrix can be expressed by the following formula

[0081]

[0082]

[0083]

[0084] Y cs =-Y cc Y ca =0

[0085]

[0086] Among them, ε XLPE is the relative dielectric constant of XLPE, εbedding is the relative dielectric constant of the armor cushion layer, ε outersheath is the relative dielectric constant of the outer sheath.

[0087] In the parameter obtaining step, a finite element model of an armored steel wire submarine cable is established, and the control equation to be solved is as follows:

[0088]

[0089] Where: is the vector differential operator; H is the magnetic field intensity (A / m); J (A / m 2 ) is the current density vector; B is the magnetic induction intensity (T); A is the magnetic vector (wb / m); σ (S / m) is the conductivity; E (V / m) is the electric field vector; J e (A / m 2 ) is the external injection current density. The voltage value can be obtained by integrating the field strength E in the formula.

[0090] By building a simplified alternative model of the submarine cable, the induced voltages of the sheath and armor are measured, and the simulation results of the finite element submarine cable model are compared with the experiment to verify the correctness of the finite element model. The induced voltages and ground loop currents of the sheath and armor are taken as reference values. The induced voltage results obtained by the two-dimensional and three-dimensional armored steel wire submarine cable models are less than 2%, and the simulation time of the three-dimensional submarine cable model is much longer than that of the two-dimensional submarine cable finite element model.

[0091] In the parameter optimization step, establish Figure 2 The finite element model of the whole armored submarine cable shown in the figure sets the magnetic permeability and resistivity of the armor layer as independent variables, the induced voltage and ground loop current of the submarine cable sheath and armor as dependent variables, and the induced voltage and ground loop current in the simulation results of the armored steel wire submarine cable finite element model as target values. The error function is set as

[0092]

[0093]

[0094] Where f1 is the error function of the induced voltage, V 整层 and is the effective value and phase of the induced voltage in the whole armored submarine cable model, V 钢丝 and is the effective value and phase of the induced voltage in the steel wire armored submarine cable model; f2 is the error function of the ground loop current, I 整层 and is the effective value and phase of the ground loop current in the whole armored submarine cable model, I 钢丝 and is the effective value and phase of the ground loop current in the steel wire armored submarine cable model.

[0095] The resistivity and permeability of the armor in the whole-layer armored submarine cable model are optimized by the IWOA algorithm to obtain calculation results close to the reference values. The equivalent armor resistivity and permeability are extracted and brought into the analytical calculation model of the submarine cable transmission line to improve the simulation accuracy.

[0096] Example 1

[0097] Feasibility verification:

[0098] Modeling of 220kV cross-linked polyethylene cable, referring to Figure 1 and Figure 2 The finite element models of two-dimensional steel wire armored submarine cable and two-dimensional full-layer armored submarine cable are established respectively. The parameters are shown in Figure 6 . A current of 100A is passed through the core, and the magnetic permeability of the armored steel wire in the steel wire armor model is set to 1500. The calculated armor open circuit induced voltage and short circuit ground loop current are used as reference values. Based on the improved whale optimization algorithm, finite element-Matlab joint simulation is performed to optimize the equivalent resistivity and magnetic permeability of the entire armor layer in the two-dimensional submarine cable model. The error between the calculated result of the entire armored submarine cable and the reference value is used as the objective function. The objective function is minimized by the optimization algorithm. The objective function is formula (10) and formula (11). Finally, the equivalent magnetic permeability of the armor layer of the entire armored submarine cable model is 7.49, and the equivalent resistivity is 4.5e-7+4.2e-7i. The imaginary part of the resistivity represents the inductance effect during magnetic field coupling.

[0099] In order to verify the effectiveness of equating the steel wire armor to the whole layer of armor, a comparative analysis before and after the equivalence was conducted. The results are shown in Figure 7 According to equations (1) to (8), the transmission line calculation model of the submarine cable is established in MATLAB. The armor resistivity and permeability are set as steel wire armor parameters (ρ = 1.38e-7, μ = 1500), and the induced voltage and ground loop current of the sheath and armor layer are calculated. The results are recorded as "not equivalent". The equivalent resistivity and permeability obtained by the improved whale algorithm are substituted into the armor parameters of the transmission line analytical model, and the impedance matrix parameter z associated with the armor layer resistivity and permeability is corrected. a，in , z a，m and z a，out , the induced voltage and ground loop current of the sheath and armor layer are calculated again, and the results are recorded as "equivalent"; as a criterion, the simulation results of the finite element model of steel wire armor are also listed in Figure 7 In the table, err neq is the error value obtained based on equations (10) and (11) when there is no equivalence, err eq is the error value after equivalent.

[0100] from Figure 7It can be seen from the results that before and after the equivalent of the resistivity and permeability of the submarine cable transmission line analytical model, the induced voltage and ground loop current have obvious differences. After the equivalent, the error value of the sheath induced voltage is reduced from 8.6 to 0.002, and the error value of the armor induced voltage is reduced from 2.27 to 0.003; the error value of the sheath ground loop current is reduced from 0.18 to 0.0004, and the error value of the armor ground loop current is reduced from 0.21 to 0.0003; after the equivalent, the calculation accuracy of the induced voltage is improved by 290%, and the error between the effective value and the reference value is less than 4.9%. The calculation accuracy of the ground loop current is improved by 44%, and the error of the effective value is less than 1.3%; on the hardware platform of Intel Xeon 2.90GHz CPU and 256G memory, the simulation time of the MATLAB transmission line analytical model is 3 seconds, the simulation time of the two-dimensional whole-layer armor finite element model is 15 seconds, and the simulation time of the three-dimensional steel wire armor finite element model is 2 hours, 38 minutes and 58 seconds. It can be seen that the use of the transmission line analytical model can significantly improve the simulation efficiency.

[0101] The above technical solutions only reflect the preferred technical solutions of the technical solutions of the present invention. Some changes that may be made to certain parts thereof by technicians in this technical field all reflect the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. A method for constructing an accurate analytical model of a submarine cable transmission line based on an IWOA algorithm, comprising a model building step, a parameter obtaining step, and a parameter optimization step. In the model building step, based on the transmission line theory, an analytical calculation model of the transmission line of the submarine cable is established in MATLAB. In the parameter obtaining step, a finite element model of a submarine cable steel wire armor is established based on the finite element method, and the induced voltage and ground loop current of the sheath and armor are calculated as reference values ​​for model optimization. In the parameter optimization step, a finite element model of the entire armor layer of the submarine cable is established based on the finite element method with reference to the simplified structure of the submarine cable. Through joint simulation with MATLAB and COMSOL, and based on the IWOA algorithm, the resistivity and permeability of the submarine cable armor layer are searched to obtain a search result close to the reference value, and the optimized resistivity and permeability are used in the analytical calculation model of the transmission line of the submarine cable to improve the simulation efficiency.

2. The method for constructing an accurate submarine cable transmission line analytical model based on the IWOA algorithm according to claim 1, characterized in that: In the model building step, the transmission line modeling formula of the cable is as follows. The voltage and current waves of the conductor at the z position along the cable axis in the transmission line model are calculated by the telegraph equation (1): V and I are defined as: V=(V c ,V s ,V a ) T I=(I c ,I s ,I a ) T (2) Among them, V c , V s , V a is the voltage of the conductor, metal sheath and armor relative to the ground. The subscripts of the current I follow the same meaning. The impedance matrix Z and the admittance matrix Y are defined as follows: For submarine cables, the common ground is the reference voltage for multi-conductor transmission line analysis. The impedance and admittance between each metal layer of the cable are shown in Figure 3. The elements in the impedance matrix Z are calculated as follows: WITH cc =from c，out +with ins，1 +with s，in -2z s，m +with s，out +with ins，2 +with a，in -2z a，m +with a，out +with ins，3 +with g WITH cs =-z sm +with s，out +with ins，2 +with a，in -2z a，m +with a，out +with ins，3 +with g WITH ss =from s，out +with ins，2 +with a，in -2z a，m +with a，out +with ins，3 +with g WITH ca =Z sa =-z a，m +with a，out +with ins，3 +with g WITH aa =from a，out +with ins，3 +with g (4) Among them, z c，out is the internal impedance of the conductor, z ins，1 is the impedance caused by the time-varying magnetic field in the XLPE insulation, z s，in is the internal impedance of the inner sheath, z s，m is the sheath mutual impedance, z s，out is the internal impedance of the outer surface of the sheath, z ins，2 is the impedance caused by the time-varying magnetic field in the insulation between the lead sheath and the armor, z ins，3 is the impedance caused by the time-varying magnetic field in the outer sheath, z g is the self-impedance of the ground loop. The transmission line analytical calculation method assumes that the submarine cable armor layer is a uniform whole layer structure when modeling the submarine cable, which is different from the metal wire armor structure of the actual submarine cable. It is necessary to optimize the parameters of the armor layer in the transmission line submarine cable model, where the associated impedance parameter of the armor layer is z a，in , z a，m and z a，out .z a，in is the internal impedance of the armor (the voltage drop on the inner surface of the sheath per unit current returned through the conductor) ρ a , μ a and m a They are the resistivity, magnetic permeability and reverse penetration depth of the armor respectively. z a，m It is the mutual impedance of the sheath, which indicates the voltage drop along the outer (inner) surface of the sheath when the unit current returns through the inner (outer) conductor. Here, the outer conductor is grounded. z a，out is the internal impedance of the outer surface of the armor (the voltage drop along the outer surface of the sheath when the current returns through the ground) The Y matrix can be expressed by the following formula AND cs -And cc AND ca =0 Among them, ε XLPE is the relative dielectric constant of XLPE, ε bedding is the relative dielectric constant of the armor cushion layer, ε outersheath is the relative dielectric constant of the outer sheath.

3. The method for constructing an accurate submarine cable transmission line analytical model based on the IWOA algorithm according to claim 1, characterized in that: In the parameter obtaining step, a finite element model of an armored steel wire submarine cable is established, and the control equation to be solved is as follows: Where: is the vector differential operator; H is the magnetic field intensity (A / m); J (A / m 2 ) is the current density vector; B is the magnetic induction intensity (T); A is the magnetic vector (wb / m); σ (S / m) is the conductivity; E (V / m) is the electric field vector; J e (A / m 2 ) is the external injection current density. The voltage value can be obtained by integrating the field strength E in the formula. A simplified alternative model of the submarine cable was built to measure the induced voltage of the sheath and armor. The simulation results of the finite element submarine cable model were compared with the experimental results to verify the correctness of the finite element model. The induced voltage and ground loop current of the sheath and armor were taken as reference values.

4. The method for constructing an accurate submarine cable transmission line analytical model based on the IWOA algorithm according to claim 1, characterized in that: In the parameter optimization step, a finite element model of the entire armored submarine cable is established, the magnetic permeability and resistivity of the armor layer are set as independent variables, the induced voltage and ground loop current of the submarine cable sheath and armor are set as dependent variables, the induced voltage and ground loop current in the simulation results of the armored steel wire submarine cable finite element model are taken as target values, and the error function is set as Where f1 is the error function of the induced voltage, V 整层 and is the effective value and phase of the induced voltage in the whole armored submarine cable model, V 钢丝 and is the effective value and phase of the induced voltage in the steel wire armored submarine cable model; f2 is the error function of the ground loop current, I 整层 and is the effective value and phase of the ground loop current in the whole armored submarine cable model, I 钢丝 and is the effective value and phase of the ground loop current in the steel wire armored submarine cable model.

5. The method for constructing an accurate submarine cable transmission line analytical model based on the IWOA algorithm according to claim 1, characterized in that: The IWOA algorithm is used to optimize the resistivity and permeability of the armor in the whole-layer armored submarine cable model. The minimum error function is used as the boundary condition to obtain the calculation results close to the reference value. The equivalent armor resistivity and permeability are extracted and brought into the analytical calculation model of the submarine cable transmission line to correct the impedance matrix parameter z associated with the armor layer resistivity and permeability. a，in , z a，m and z a，out , improve simulation accuracy.

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