Method, device, equipment and medium for calculating sheath induced voltage and circulating current of high-voltage alternating-current submarine cable grounding system

Abstract

The invention discloses a sheath induced voltage and circulating current calculation method, device and equipment of a high-voltage alternating-current submarine cable grounding system and a medium. The method comprises the following steps: firstly, constructing a series impedance matrix and a parallel admittance matrix of a unit length high-voltage alternating-current submarine cable; secondly, performing series expansion on the high-voltage alternating-current submarine cable in a double-end grounding mode according to a telegraph equation in a frequency domain to obtain a node admittance matrix of the submarine cable in unit length; then deriving to obtain a cascading formula of a unit length submarine cable without a middle grounding point and with middle grounding, and combining the node admittance matrix of the unit length submarine cable to obtain a complete node admittance matrix of the submarine cable grounding system; and according to the submarine cable voltage and current boundary conditions and the complete node admittance matrix of the submarine cable grounding system, constructing a sheath induced voltage and circulating current calculation model of the high-voltage alternating-current submarine cable grounding system considering the anchoring device under the double-end grounding condition. According to the invention, the sheath induced voltage and circulation distribution of the high-voltage AC submarine cable grounding system can be accurately calculated.

Description

Technical Field

[0001] The present invention belongs to the field of power transmission, and in particular relates to a method, device, equipment and medium for calculating sheath induced voltage and circulating current of a high-voltage AC submarine cable grounding system taking into account an anchoring device. Background Art

[0002] After commissioning, high-voltage AC submarine cable systems are subject to not only electric, mechanical, and thermal stresses, but also marine environmental factors. These factors, in particular, increase the contact resistance of the anchoring system, causing heating and even accelerating thermal aging of the insulation, severely reducing the service life of the cable. Recently, several incidents have occurred in China where overheating of the anchoring system has caused the main insulation of the cable to break down. These incidents have exposed common problems such as inadequate design considerations for the grounding system of high-voltage AC cables, incomplete condition monitoring, and difficulty in fully identifying potential faults. These issues have severely impacted the reliability of the cable and introduced numerous new challenges to its safe operation. The primary reason for these issues is that as the current flowing through the cable system increases, the induced voltage and circulating current in the cable also increase, potentially limiting the cable's current carrying capacity. When using long-distance, high-capacity marine transmission technology, the electromagnetic coupling between the various phases of the cable increases, leading to increased induced voltage on the sheath, which not only endangers personal safety but can even cause breakdown of the outer sheath. On the other hand, the existence of induced voltage in the submarine cable line will cause circulating current on the sheath. Excessive sheath circulating current will cause heat loss in the submarine cable, resulting in local heating of the submarine cable and limiting the increase in the current carrying capacity of the submarine cable.

[0003] Therefore, it is urgent to accurately calculate the induced voltage and circulating current in the sheath of the high-voltage AC submarine cable, and the influence of the anchoring device must be considered during the calculation. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the defects of the above-mentioned prior art and provide a method for calculating the sheath induced voltage and circulating current of a high-voltage AC submarine cable grounding system taking into account the anchoring device, so as to accurately calculate the sheath induced voltage and circulating current distribution of the high-voltage AC submarine cable grounding system, thereby providing a basis for the subsequent high-voltage AC submarine cable system engineering design.

[0005] In order to achieve the above-mentioned purpose, the present invention adopts a technical solution.

[0006] In a first aspect, the present invention provides a method for calculating induced voltage and circulating current in a high-voltage AC submarine cable sheath grounding system, comprising:

[0007] The series impedance matrix and parallel admittance matrix of unit length high-voltage AC submarine cable without anchoring device and with anchoring device are constructed respectively;

[0008] Using the series impedance matrix and the parallel admittance matrix, combined with the frequency domain telegraph equation, a series expansion is performed on a unit length of submarine cable in a double-end grounding mode to obtain a unit length submarine cable node admittance matrix;

[0009] The cascade formula of unit-length submarine cables with and without intermediate grounding is derived, and the complete nodal admittance matrix of the high-voltage AC submarine cable grounding system is obtained by combining the nodal admittance matrix of the unit-length submarine cable.

[0010] Based on the voltage and current boundary conditions of the submarine cable and the complete node admittance matrix of the high-voltage AC submarine cable grounding system, a calculation model for the sheath induced voltage and circulating current of the high-voltage AC submarine cable grounding system with double-terminal grounding and anchoring device is constructed. The sheath induced voltage and circulating current are calculated based on the model.

[0011] Furthermore, the construction process of the series impedance matrix and parallel admittance matrix of the unit length high-voltage AC submarine cable is as follows:

[0012] Based on the geometric structure of the HVAC submarine cable grounding system and the material parameters of each dielectric layer, the structure of the anchoring device and its connection method with the HVAC submarine cable are analyzed, and the equivalent circuit of the anchoring device is obtained. Taking into account the electromagnetic coupling characteristics between the HVAC submarine cables and the influence of the grounding method of the HVAC submarine cable, the series impedance matrix and parallel admittance matrix per unit length of the HVAC submarine cable without and with the anchoring device are constructed respectively.

[0013] Furthermore, the specific construction process of the series impedance matrix of the unit length high-voltage AC submarine cable is as follows:

[0014] Obtain the loop current matrix equation of a single-phase single-core high-voltage AC submarine cable without anchoring devices;

[0015] The series impedance matrix of the single-phase single-core high-voltage AC submarine cable loop per unit length without anchoring device is obtained from the voltage and current telegraph equations of the single-phase single-core submarine cable per unit length and the current matrix equation of the single-phase single-core high-voltage AC submarine cable loop without anchoring device.

[0016] The connection mode of the anchoring device and the equivalent circuit of the anchoring are analyzed to obtain the series impedance matrix of the unit length single-phase single-core high-voltage AC submarine cable including the anchoring device.

[0017] The series impedance matrix of unit length single-phase single-core high-voltage AC submarine cable is extended to three-phase submarine cable. First, the calculation formula of the series impedance matrix of unit length high-voltage AC submarine cable without anchoring device is obtained, and then the calculation formula of the series impedance matrix of unit length high-voltage AC submarine cable with anchoring device is obtained.

[0018] Furthermore, the parallel admittance matrix of the unit length high-voltage AC submarine cable is constructed as follows:

[0019] Obtain the node voltage matrix equation of a single-phase single-core high-voltage AC submarine cable without anchoring devices;

[0020] The parallel admittance matrix of the single-phase single-core high-voltage AC submarine cable per unit length without anchoring device is obtained from the voltage and current telegraph equations of the single-phase single-core submarine cable per unit length and the node voltage matrix equation of the single-phase single-core high-voltage AC submarine cable without anchoring device.

[0021] The connection mode of the anchoring device and the equivalent circuit of the anchoring are analyzed to obtain the parallel admittance matrix of the unit length single-phase single-core high-voltage AC submarine cable including the anchoring device.

[0022] The parallel admittance matrix of unit length single-phase single-core high-voltage AC submarine cable is extended to three-phase submarine cable. First, the calculation formula of the parallel admittance matrix of unit length high-voltage AC submarine cable without anchoring device is obtained, and then the calculation formula of the parallel admittance matrix of unit length high-voltage AC submarine cable with anchoring device is obtained.

[0023] Furthermore, the specific construction process of the node admittance matrix of the unit length submarine cable is as follows:

[0024] First, according to the telegraph equation in the frequency domain, the frequency domain equation of the transmission line is obtained:

[0025]

[0026] Among them, U x and I x They represent the voltage vector and current vector of the line conductor at point x in time t, Z is the series impedance matrix of the unit length high-voltage AC submarine cable, and Y is the parallel admittance matrix of the unit length high-voltage AC submarine cable;

[0027] Then, according to the boundary conditions at the beginning and end, we have:

[0028] At the beginning, that is, when x=0, U x =U sd , I x =I sd ;

[0029] At the end, that is, when x=l, U x =U md , I x =I md ;

[0030] Substitute this into the differential equation to obtain:

[0031]

[0032] Among them, U sd and I sd are the voltage vector and current vector of the starting node of the submarine cable respectively; Umd and I md are the voltage vector and current vector at the end node of the submarine cable respectively, where Γ is the propagation parameter, and the calculation expression is:

[0033]

[0034] Finally, the hyperbolic function is introduced through matrix transformation to obtain the node admittance matrix of the unit length submarine cable:

[0035]

[0036] Furthermore, the derivation process of the cascade formula of the unit length submarine cable with and without intermediate connection points is as follows:

[0037] Combined with the node admittance matrix of the unit length submarine cable, the complete node admittance matrix of the high voltage AC submarine cable grounding system is obtained;

[0038] First, for the admittance matrix Y without intermediate nodes a and Y b The specific formula is as follows:

[0039]

[0040] Among them, I S , I P ″ are Y a 、Y b The current at the head end of the corresponding submarine cable segment, I P ′、I R Y a 、Y b The current at the end of the corresponding submarine cable segment, U S 、U P ′ are Y a 、Y b The voltage matrix of the first end of the corresponding submarine cable to the ground, U P 、U R Y a 、Y b The voltage matrix of the end of the corresponding section of submarine cable to the ground, Y S 、Y m Y a 、Y b One quarter matrix of p Y a A quarter matrix of

[0041] For two cascaded submarine cables, the currents flowing from both ends into their connection are equal in magnitude and opposite in direction, and the relationship is:

[0042] I′ P +I′ P′=0

[0043] The cascade formula of the admittance matrix without intermediate nodes is obtained:

[0044]

[0045] Then, for a cascade with an intermediate ground node, the specific formula is:

[0046]

[0047] Among them, Y1′ and Y2′ are the admittance matrices including the intermediate ground nodes, and E ij 、F ij , G ij 、H ij It is the submatrix of the quarter node admittance matrix E, F, G, H of Y1′, representing the intermediate matrix in the node admittance matrix, i, j = 1, 2; Q ij 、W ij 、S ij 、R ij is the submatrix of the quarter node admittance matrix Q, W, S, R of Y2′, representing the intermediate matrix in the node admittance matrix; E 11 、F 11 , G 11 、H 11 , Q 11 、W 11 、S 11 、R 11 The order of E is (n-1)×(n-1); 12 、F 12 , G 12 、H 12 , Q 12 、W 12 、S 12 、R 12 The order of E is (n-1)×1; 21 、F 21 , G 21 、H 21 , Q 21 、W 21 、S 21 、R 21 The order of E is 1×(n-1); 22 、F 22 , G 22 、H 22 , Q 22 、W 22 、S 22 、R 22 The order is 1×1, and n is the number of submarine cables;

[0048] in,

[0049]

[0050] For the admittance matrices Y1′ and Y2′ containing the intermediate ground node, the admittance matrix after the cascade of the admittance matrices of the Y1′ and Y2′ nodes is obtained:

[0051]

[0052] Where T1 and T2 are Y′ 12 The intermediate matrix of is expressed as follows:

[0053] T1=(H 11 +Q 11 ) -1 G 11 ,

[0054] T2=(H 11 +Q 11 ) -1 W 11 ,

[0055] At this point, the node admittance matrices with and without intermediate locations are constructed by the cascade algorithm.

[0056] Furthermore, the construction process of the sheath induced voltage and circulating current calculation model of the high-voltage AC submarine cable grounding system taking into account the anchor device under the double-end grounding method is as follows:

[0057] First, the voltage and current values U of the sending and receiving sections of the jth section of the i-th section of the high-voltage AC submarine cable are calculated. S,i,j 、U R,i,j , I S,i,j and I R,i,j Perform matrix transformation and obtain the following formula:

[0058]

[0059] Among them, Y S,i,j 、Y R,i,j is a symmetric quarter matrix, i=1,2,3;

[0060] Secondly, the above formula is used to calculate the cable section containing the anchoring device to obtain the voltage and current U of the jth receiving end of the i-th high-voltage AC submarine cable. R,i,j , I R,i,j , and then use the following formula to calculate the induced voltage and circulating current of the remaining sections of the submarine cable without anchoring devices:

[0061]

[0062] I R ″ ,i,j 、UR ″ ,i.j They represent the calculated induced voltage and circulating current of the submarine cable section without anchoring devices;

[0063] According to the induced voltage and circulating current, the induced voltage and circulating current of the high-voltage AC submarine cable grounding system are derived using a cascade algorithm.

[0064] In a second aspect, the present invention provides a high-voltage AC submarine cable sheath induced voltage and circulating current calculation system, comprising:

[0065] Series impedance matrix and parallel admittance matrix construction unit: constructs the series impedance matrix and parallel admittance matrix of the unit length high-voltage AC submarine cable without anchoring device and with anchoring device respectively;

[0066] A node admittance matrix acquisition unit is configured to perform series expansion on a unit-length submarine cable in a double-end grounding mode by utilizing the series impedance matrix and the parallel admittance matrix in combination with the frequency-domain telegraph equation to obtain the node admittance matrix of the unit-length submarine cable.

[0067] Complete node admittance matrix acquisition unit: derives the cascade formula of unit-length submarine cables with and without intermediate grounding points, and combines the node admittance matrix of the unit-length submarine cable to obtain the complete node admittance matrix of the high-voltage AC submarine cable grounding system;

[0068] Induced voltage and circulating current calculation unit: Based on the voltage and current boundary conditions of the submarine cable and the complete node admittance matrix of the high-voltage AC submarine cable grounding system, a sheath induced voltage and circulating current calculation model for the high-voltage AC submarine cable grounding system under double-terminal grounding mode and including the anchor device is constructed, and the sheath induced voltage and circulating current are calculated based on the said model.

[0069] In a third aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the method for calculating the sheath induced voltage and circulating current of the high-voltage AC submarine cable grounding system are implemented.

[0070] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for calculating the sheath induced voltage and circulating current of the high-voltage AC submarine cable grounding system.

[0071] Compared with the prior art, the present invention has the following beneficial effects:

[0072] (1) High-voltage AC submarine cables differ greatly from traditional submarine cables in terms of installation environment, installation method, and interlayer coupling method. The present invention considers the combined effects of the above-mentioned factors and can more accurately calculate and evaluate the steady-state characteristics of the high-voltage AC submarine cable system.

[0073] (2) The traditional finite element simulation calculation method can only simulate and analyze the voltage and current at special positions of the submarine cable, and cannot simulate and analyze the sheath voltage and circulating current values of the submarine cable system; the present invention can calculate and solve the induced voltage and circulating current of the entire high-voltage AC submarine cable system, providing a basis for the subsequent high-voltage AC submarine cable system engineering design.

[0074] (3) The traditional method significantly increases the calculation time during the calculation process due to the continuous increase in the order of its node admittance matrix. However, the present invention is based on a cascade calculation method and takes into account the influence of the laying method of the high-voltage AC submarine cable system. The grounded and ungrounded parts of the submarine cable system are divided and the corresponding cascade formula is obtained, which reduces the time required for calculation.

[0075] (4) In actual engineering applications, AC submarine cable systems require anchoring devices for stability. Existing calculation models do not consider the impact of this part. The present invention obtains its node admittance matrix by studying the equivalent model of the anchoring device, constructs a sheath induced voltage and circulating current calculation model for high-voltage AC submarine cables taking into account the anchoring device, and improves the application scope of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 Schematic diagram of the flow chart of the method for calculating the sheath induced voltage and circulating current of the high-voltage AC submarine cable system of the present invention;

[0077] Figure 2 This is a circuit equivalent model diagram of a single high-voltage AC submarine cable system without an anchoring device in a specific embodiment of the present invention;

[0078] Figure 3 Schematic diagram of the equivalent capacitance and equivalent resistance circuit model of a single high-voltage AC submarine cable in a specific embodiment of the present invention;

[0079] Figure 4 This is an equivalent model diagram of a single high-voltage AC submarine cable system loop including an anchoring device section in a specific embodiment of the present invention;

[0080] Figure 5 Schematic diagram of the connection of a high-voltage AC submarine cable with double-end grounding in a specific embodiment of the present invention;

[0081] FIG6( a ) is a schematic diagram of the circulation distribution of the A-phase sheath of the high-voltage AC submarine cable taking into account the anchoring device in a specific embodiment of the present invention;

[0082] FIG6( b ) is a schematic diagram of the induced voltage distribution of the phase A sheath of the high-voltage AC submarine cable taking into account the anchoring device in a specific embodiment of the present invention;

[0083] Figure 7It is a logical structure diagram of a computer device provided in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0084] In order to describe the present invention in more detail, the present invention will be further described below with reference to the accompanying drawings and specific implementation methods.

[0085] Example 1

[0086] like Figure 1 As shown, this embodiment is a method for calculating the sheath induced voltage and circulating current of a high-voltage AC submarine cable system taking into account the anchoring device, and the steps are as follows:

[0087] Step 1: Based on the geometric structure of the HVAC submarine cable grounding system and the material parameters between each dielectric layer, the structure of the anchoring device and its connection method with the HVAC submarine cable are analyzed to obtain the equivalent circuit of the anchoring device. Taking into account the electromagnetic coupling characteristics between the HVAC submarine cables and the influence of the grounding method of the HVAC submarine cable, the series impedance matrix and parallel admittance matrix of the unit length HVAC submarine cable without and with the anchoring device are constructed respectively.

[0088] The equivalent model of a single high-voltage AC submarine cable loop without anchoring device is as follows: Figure 2 As shown, first, due to the different electrical properties of the dielectric materials between the submarine cable layers, there is electromagnetic coupling between them. The calculation expression of the impedance matrix of a single submarine cable loop is as follows:

[0089]

[0090] Where u1 is the voltage between the core and the earth, u2 is the voltage between the sheath and the earth, u3 is the voltage between the armor and the earth, i1 is the current of the core-sheath insulation layer-sheath layer loop (i.e., the first loop), i2 is the current of the sheath layer-armor insulation layer-armor loop (i.e., the second loop), i3 is the current of the armor-earth insulation layer-earth loop (i.e., the third loop), and Z ii (i=1,2,3) is the self-impedance per unit length of the i-th loop, Z ij (i, j = 1, 2, 3) is the mutual impedance per unit length between the i-th loop and the j-th loop.

[0091] Then, the self-impedance in the series impedance matrix of a single-core high-voltage AC submarine cable per unit length without an anchoring device is determined using the following expression:

[0092]

[0093] Among them, Z c is the internal impedance of the submarine cable core per unit length; Z CS-in Z is the series impedance of the first loop cable core per unit length caused by the change of magnetic field;SA-in is the series impedance of the second loop; Z AG-in is the series impedance of the third loop; Z GA-in Represents the series impedance of the third loop; Z S-in is the internal series impedance of the sheath layer; Z S-out is the external series impedance of the sheath layer; Z A-in is the internal series impedance of the armor layer; Z A-out is the external series impedance of the armor layer; Z S-mutual is the series impedance caused by the magnetic field in the first loop; Z A-mutual is the series impedance caused by the magnetic field in the second circuit; Z g It is the sum of external reactance and lossy earth impedance.

[0094] The specific expressions of the impedances of the three loops in formula (2) are as follows:

[0095]

[0096] In formula (3), μ c 、μ ins 、μ out-ins 、μ out2-ins are the magnetic permeabilities of the submarine cable core, core-sheath insulation layer, sheath-armor insulation layer, and armor-earth insulation layer, respectively; k is an arbitrary constant for optimizing the low-frequency formula, usually taken as 0.777; ω is the angular frequency; R1, R2, R3, R4, R5, and R6 are the radii of the submarine cable core, core-sheath insulation layer, submarine cable sheath layer, sheath-armor insulation layer, armor, and armor-earth insulation layer, respectively; m A is the reciprocal of the composite penetration depth of the submarine cable armor; μ ins-out is the magnetic permeability of the submarine cable sheath-armor insulation layer; ρ c , ρ s , ρ A are the resistivity of the submarine cable core, submarine cable sheath and submarine cable armor respectively; m c 、m s are the reciprocals of the composite penetration depths of the submarine cable core and the submarine cable sheath respectively; ρ c ' is the corrected submarine cable resistivity, determined by formula (4):

[0097]

[0098] Where A c Indicates the cross-sectional area of the conductor;

[0099] The mutual impedance per unit length Z between the core-ground loop and the shield-ground loop 12 Calculated by formula (5):

[0100] Z 12 =zS-out +z SA-in +z A-out +z A-in +z AG-in +z g -z S-mutual -2z A-mutual (5)

[0101] Mutual impedance per unit length Z between the core-earth loop and the armor-earth loop 13 Calculated by formula (6):

[0102] Z 13 =z A-in +z AG-in +z g -z A-mutual (6)

[0103] The mutual impedance per unit length Z between the shield layer-ground loop and the armor layer-ground loop 23 Calculated by formula (7):

[0104] Z 23 =z A-out +z AG-in +z g (7)

[0105] Based on the impedance matrix of a single submarine cable loop without an anchoring device, the impedance matrix of the submarine cable loop without an anchoring device is obtained from the telegraph equation between the voltage, current and unit length Δx of a single single-core submarine cable:

[0106]

[0107] Among them, u c is the voltage between the core and the earth, u s is the voltage between the sheath and the earth, u a is the voltage between the armor and the earth, i c is the current of the core-inner insulation layer-sheath layer loop, i s is the sheath layer-outer insulation layer-armor loop current, i a is the armor-outer sheath-earth loop current, z cc is the core self-impedance per unit length, z cs is the mutual impedance per unit length between the core, inner insulation and sheath, z ca is the mutual impedance per unit length between core-sheath-armor, z ss is the sheath self-impedance per unit length, z sa is the mutual impedance per unit length between sheath-outer insulation-armor, z aa is the self-impedance per unit length of the armor layer. Its calculation formula is as follows:

[0108]

[0109] Where z S-out External series impedance of the sheath layer;

[0110] Secondly, the connection mode of the anchoring device and the equivalent circuit of the anchoring are analyzed, and the impedance matrix of the submarine cable loop including the anchoring device is obtained as shown in formula (10):

[0111]

[0112] Among them, Z 33 ' is the self-impedance per unit length of the loop containing the anchoring device.

[0113] The self-impedance in the impedance matrix per unit length of the high-voltage AC submarine cable is determined using the following expression:

[0114] Z3'3=z A-in +z AG-in +z g +z mg (11)

[0115] Among them, Z mg is the anchoring impedance.

[0116] Finally, the impedance matrix of a single single-core submarine cable is extended to a three-phase system. First, the calculation formula of the series impedance matrix of a unit length high-voltage AC submarine cable excluding the anchoring device is obtained, as shown in formula (12):

[0117]

[0118] Secondly, the calculation formula of the series impedance matrix of the unit length high-voltage AC submarine cable including the anchoring device is obtained as shown in formula (13):

[0119]

[0120] Among them, u ci (i=1,2,3) are the voltages of the three-phase cores of the submarine cable A, B, and C to the ground, u si (i=1,2,3) are the voltages of the three-phase sheath to ground of submarine cables A, B, and C respectively, u ai (i=1,2,3) are the three-phase armor-to-ground voltages of submarine cables A, B, and C respectively; i ci (i=1,2,3) are the currents flowing through the three-phase cores of the submarine cable A, B, and C respectively, i si (i=1,2,3) are the currents flowing through the three-phase sheaths of submarine cables A, B, and C respectively, i ai (i=1,2,3) are the currents flowing through the three-phase armor of submarine cables A, B, and C respectively; z cicj 、z cisj 、zciaj 、z sisj 、z siaj 、z sicj 、z aiaj 、z aicj 、z aisj (i, j = 1, 2, 3) is the mutual impedance per unit length of the three-phase A, B, and C lines of the submarine cable.

[0121] Among them, z c1c1 、z c2c2 、z c3c3 、z s1s1 、z s2s2 、z s3s3 、z a1a1 、z a2a2 、z a3a3 、z a3a3 ′ can be calculated using the impedance matrix formula of a single submarine cable, and since the three-phase submarine cables are the same, we can get: c1c1 =z c2c2 =z c3c3 , z s1s1 =z s2s2 =z s3s3 , z a 1 a 1=z a 2 a 2=z a 3 a 3.

[0122] The mutual inductance between phases is a function of distance. The distance between the core of phase A and the core of phase B is almost equal to the distance between the core of phase A and the shield of phase B. The same conclusion applies to other phases, so: c1c2 ≈z c1s2 ≈z s1c2 ≈z s1s2 , z c1c3 ≈z c1s3 ≈z s1c3 ≈z s1s3 , z c2c3 ≈z c2s3 ≈z s2c3 ≈z s2s3 , the same equivalent exists in the armor layer.

[0123] Equations (12) and (13) can be further simplified to obtain simplified series impedance matrices as shown in Equations (14) and (15):

[0124]

[0125] Among them, u ci (i=1,2,3) are the voltages of the three-phase cores of the submarine cable A, B, and C to the ground, usi (i=1,2,3) are the voltages of the three-phase sheath to ground of submarine cables A, B, and C respectively, u ai (i=1,2,3) are the three-phase armor-to-ground voltages of submarine cables A, B, and C respectively; i ci (i=1,2,3) are the currents flowing through the three-phase cores of the submarine cable A, B, and C respectively, i si (i=1,2,3) are the currents flowing through the three-phase sheaths of submarine cables A, B, and C respectively, i ai (i=1,2,3) are the currents flowing through the three-phase armor of submarine cables A, B, and C respectively; z cicj 、z cisj 、z ciaj 、z sisj 、z siaj 、z sicj , (i,j=1,2,3) is the mutual impedance per unit length of the three-phase A, B, and C lines of the submarine cable.

[0126] Then the parallel admittance matrix of the submarine cable per unit length is established, and the equivalent capacitance model of a single submarine cable is as follows: Figure 3 shown.

[0127] First, solve the parallel admittance matrix of a single submarine cable, which is expressed as shown in formula (16):

[0128]

[0129] Among them, u c 、u s 、u a are the voltages of the core, sheath and armor layer to ground, i c 、i s 、i a are the incident currents on the core, sheath and armor respectively, y CC is the core self-admittance; y CS is the mutual admittance between the core and the sheath layer; SS is the self-admittance of the sheath layer; y SA is the mutual admittance between the sheath layer and the armor layer; y AA It is the self-admittance of the armor layer.

[0130] The expressions are shown in formula (17):

[0131]

[0132] Among them, C CS 、C SA 、C AG are the capacitances between the submarine cable core and the sheath, the submarine cable sheath and the armor, and the submarine cable armor and the earth, respectively. The calculation formula is shown in formula (18):

[0133]

[0134] Where ε0 is the dielectric constant of vacuum, ε in is the relative dielectric constant of the inner insulation layer, ε out is the relative dielectric constant of the outer insulation layer.

[0135] Finally, the admittance matrix of a single submarine cable is extended to the three-phase submarine cable system, and the calculation formula of the parallel admittance matrix of the high-voltage AC submarine cable is obtained as follows:

[0136]

[0137] Among them, i c1 、i c2 、i c3 are the currents flowing through the three-phase cores of the submarine cable A, B, and C, i s1 、i s2 、i s3 are the currents flowing through the three-phase sheaths of submarine cables A, B, and C, respectively, i a1 、i a2 、i a3 are the currents flowing through the three-phase armor of submarine cables A, B, and C, respectively, and y cici 、y sisi 、y aiai (i=1,2,3) are the parallel admittance self-impedance of the core, sheath and armor of the three-phase submarine cable A, B and C per unit length respectively; y cisj 、y siaj 、y aisj 、y sicj (i, j = 1, 2, 3) are the parallel admittance mutual impedances between the core, sheath, and armor of the three-phase submarine cable A, B, and C per unit length; u ci 、u si 、u ai (i=1,2,3) are the voltages of the core, sheath and armor layer to ground respectively.

[0138] Step 2: Perform series approximation on the unit length submarine cable line and construct the node admittance matrix of the unit length submarine cable line. The process is as follows:

[0139] First, based on the telegraph equation of the submarine cable in the frequency domain, the frequency domain equation of the transmission line is obtained:

[0140]

[0141] Among them, U x and I x They represent the voltage vector and current vector of the line conductor at point x in time t, Z is the series impedance matrix per unit length of the submarine cable system, and Y is the loop impedance matrix per unit length of the submarine cable system;

[0142] The boundary conditions at the beginning and end of the circuit are combined to solve the differential equation (20), and the following relationship is obtained:

[0143] At the beginning of the submarine cable, that is, when x = 0, there exists: U x =U sd , I x =I sd ;

[0144] At the end of the submarine cable, that is, when x = l, there exists: U x =U md , I x =I md ;

[0145] Substituting the above boundary conditions into the differential equations, we can obtain:

[0146]

[0147] Among them, U sd and I sd are the voltage vector and current vector of the starting node of the submarine cable respectively; U md and I md are the voltage vector and current vector at the end node of the submarine cable respectively, where Γ is the propagation parameter, and the calculation expression is:

[0148]

[0149] By introducing the hyperbolic function through matrix transformation, the node admittance matrix of the unit length submarine cable line is obtained:

[0150]

[0151] Perform Laurent series expansion on the hyperbolic functions coth(Γl) and csch(Γl) in formula (23):

[0152]

[0153]

[0154] Among them, B 2i is the Bernoulli number.

[0155] Step 3: Derived the cascade formula of AC submarine cables with and without intermediate nodes, and combined with the node admittance matrix of the unit length submarine cable line to obtain the complete node admittance matrix of the AC submarine cable grounding system taking into account the anchor device.

[0156] The submarine cable grounding system of the present invention is a double-end grounding system, and its structure is as follows: Figure 5As shown, the cascade algorithm with and without intermediate locations is described.

[0157] First, for the admittance matrix Y without indirect locations a and Y b The specific method of cascading is as follows:

[0158]

[0159] Among them, I S , I P ″ are Y a 、Y b The current at the head end of the corresponding submarine cable segment, I P ′、I R Y a 、Y b The current at the end of the corresponding submarine cable segment, U S 、U P ′ are Y a 、Y b The voltage between the first end of the corresponding section of submarine cable and the ground, U P 、U R Y a 、Y b The voltage at the end of the corresponding section of submarine cable to ground, Y S 、Y m Y a 、Y b One-quarter matrix, Y P Y a A quarter matrix of ;

[0160] For two cascaded submarine cables, the currents flowing from both ends into their connection are equal in magnitude and opposite in direction, and the relationship is:

[0161] I′ P +I′ P ′=0 (28)

[0162] The cascade formula of the admittance matrix without intermediate nodes is obtained:

[0163]

[0164] Then, for a cascade connection with an intermediate ground node, the specific method is:

[0165]

[0166] Among them, Y1′ and Y2′ are the admittance matrices including the intermediate ground nodes, and E ij 、F ij , G ij 、H ij(i, j = 1, 2) is the sub-matrix of the quarter node admittance matrix E, F, G, H of Y1′, representing the intermediate matrix in the node admittance matrix, Q ij 、W ij 、S ij 、R ij (i, j = 1, 2) is the sub-matrix of the quarter node admittance matrix Q, W, S, R of Y2′, representing the intermediate matrix in the node admittance matrix; E 11 、F 11 , G 11 、H 11 , Q 11 、W 11 、S 11 、R 11 The order of is (n-1)×(n-1);

[0167] E 12 、F 12 , G 12 、H 12 , Q 12 、W 12 、S 12 、R 12 The order of E is (n-1)×1; 21 、F 21 , G 21 、H 21 , Q 21 、W 21 、S 21 、R 21 The order of E is 1×(n-1); 22 、F 22 , G 22 、H 22 , Q 22 、W 22 、S 22 、R 22 The order is 1×1, and n is the number of submarine cables;

[0168] in,

[0169]

[0170] For the admittance matrices Y1′ and Y2′ containing the intermediate ground node, the admittance matrix after the cascade of the admittance matrices of the Y1′ and Y2′ nodes is obtained:

[0171]

[0172] Where T1 and T2 are Y′ 12 The intermediate matrix of is expressed as follows:

[0173] T1=(H11 +Q 11 ) -1 G 11 (34)

[0174] T2=(H 11 +Q 11 ) -1 W 11 (35)

[0175] Finally, formula (29) and formula (33) are used to obtain the cascade algorithm with and without intermediate locations.

[0176] Step 4: Based on the boundary conditions and the node admittance matrix of the AC submarine cable grounding system, the unit length AC submarine cable including the anchoring device is divided into two parts. A calculation model for the sheath induced voltage and circulating current of the AC submarine cable grounding system including the anchoring device under the double-end grounding method is constructed. The sheath induced voltage and circulating current of the AC submarine cable grounding system including the anchoring device are calculated based on the model.

[0177] First, the voltage and current values U of the sending and receiving sections of the jth section of the AC submarine cable are calculated. S,i,j 、U R,i,j , I S,i,j , I R,i,j Perform matrix transformation and obtain the following formula:

[0178]

[0179] Among them, Y S,i,j 、Y R,i,j (i=1,2,3) is a symmetric quarter matrix;

[0180] The above formula can be used to calculate the induced voltage and circulating current distribution per unit length of AC submarine cable, and the induced voltage and circulating current of the AC submarine cable system can be derived using the cascade algorithm.

[0181] Figures 6(a) and 6(b) are schematic diagrams of the sheath induced voltage and sheath circulating current distribution of phase A with and without intermediate connection points under double-end grounding. The present invention can obtain induced voltage and circulating current distribution curves. Based on the geometric structural characteristics of the high-voltage AC submarine cable and the parameters of the dielectric materials between the layers, and considering the electromagnetic coupling characteristics between the AC submarine cables and the influence of the AC submarine cable grounding method, a calculation model of the unit length series impedance matrix and parallel admittance matrix of the submarine cable with and without anchoring devices is constructed. The obtained series impedance matrix and parallel admittance matrix model of the unit length submarine cable are combined with the frequency domain telegraph equation to perform Laurent series on the unit length submarine cable line under double-end grounding to construct the node admittance matrix of the unit length submarine cable line. Based on this node admittance matrix, combined with the submarine cable cascade formula without and with intermediate connection points, the node admittance matrix of the entire high-voltage AC submarine cable system is obtained. Finally, based on the boundary conditions and the node admittance matrix of the entire line, a calculation model of the sheath induced voltage and circulating current of the entire high-voltage AC submarine cable under double-end grounding conditions is constructed. As shown in Figure 6(a), the sheath induced voltage first increases and then decreases with increasing distance, reaching a maximum value of 98V at the middle of the line. The sheath induced current of phase A with an intermediate connection point increases with increasing distance, then decreases to 0kV, then rapidly increases again and finally decreases to 0V at the terminal of the submarine cable system at 18km. As shown in Figure 6(b), the sheath induced current of phase A without an intermediate connection point decreases with increasing distance, from a maximum value of 1037A to 884A, with a minimum value located approximately 18km from the line head end. The sheath induced current of phase A with an intermediate connection point decreases with increasing distance, then suddenly increases at around 9km, and then decreases again. In summary, the calculation method of the present invention is capable of calculating the sheath induced voltage and circulating current of multi-circuit submarine cable systems.

[0182] Example 2

[0183] This embodiment provides a high-voltage AC submarine cable sheath induced voltage and circulating current calculation system, which consists of a series impedance matrix and parallel admittance matrix construction unit, a node admittance matrix acquisition unit, a complete node admittance matrix acquisition unit, and an induced voltage and circulating current calculation unit.

[0184] Series impedance matrix and parallel admittance matrix construction unit: construct the series impedance matrix and parallel admittance matrix of unit length high-voltage AC submarine cable without anchoring device and with anchoring device respectively.

[0185] Node admittance matrix acquisition unit: using the series impedance matrix and parallel admittance matrix, combined with the telegraph equation in the frequency domain, the unit length submarine cable under the double-end grounding mode is subjected to series expansion to obtain the node admittance matrix of the unit length submarine cable.

[0186] Complete node admittance matrix acquisition unit: derives the cascade formula of unit-length submarine cables with and without intermediate grounding points, and combines the node admittance matrix of unit-length submarine cables to obtain the complete node admittance matrix of the high-voltage AC submarine cable grounding system.

[0187] Induced voltage and circulating current calculation unit: Based on the boundary conditions and the complete node admittance matrix of the high-voltage AC submarine cable grounding system, a sheath induced voltage and circulating current calculation model for the high-voltage AC submarine cable grounding system under double-terminal grounding mode including the anchor device is constructed, and the sheath induced voltage and circulating current are calculated based on the model.

[0188] It should be noted that each unit in the above-mentioned high-voltage AC submarine cable sheath induced voltage and circulating current calculation system can be fully or partially implemented by software, hardware and their combination. The above-mentioned units can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory in the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above-mentioned units. For the specific definition of a high-voltage AC submarine cable sheath induced voltage and circulating current calculation system, please refer to the definition of a high-voltage AC submarine cable sheath induced voltage and circulating current calculation method (i.e., Example 1) above. The two have the same functions and effects and will not be repeated here.

[0189] Example 3

[0190] This embodiment provides a computer device, comprising: at least one processor; and a memory communicatively connected to the at least one processor. The memory stores a computer program executable by the at least one processor, wherein the computer program, when executed by the at least one processor, causes the electronic device to perform the method according to Embodiment 1 of the present invention.

[0191] Example 4

[0192] This embodiment provides a non-transitory computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor of a computer, is used to cause the computer to perform the method according to embodiment 1 of the present invention.

[0193] refer to Figure 7, a block diagram of an electronic device 400 that can serve as a server or client of the present invention will now be described, which is an example of a hardware device that can be applied to various aspects of the present invention. The electronic device is intended to represent various forms of digital electronic computer devices, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present invention described and / or required herein.

[0194] like Figure 7 As shown, electronic device 400 includes a computing unit 401, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 402 or a computer program loaded from a storage unit 408 into a random access memory (RAM) 403. Various programs and data required for the operation of electronic device 400 can also be stored in RAM 403. Computing unit 401, ROM 402, and RAM 403 are connected to each other via a bus 404. An input / output (I / O) interface 405 is also connected to bus 404.

[0195] Multiple components within electronic device 400 are connected to I / O interface 405, including an input unit 406, an output unit 407, a storage unit 408, and a communication unit 409. Input unit 406 can be any type of device capable of inputting information into electronic device 400. Input unit 406 can receive input numeric or character information and generate key input signals related to user settings and / or function control of the electronic device. Output unit 407 can be any type of device capable of presenting information and may include, but is not limited to, a display, a speaker, a video / audio output terminal, a vibrator, and / or a printer. Storage unit 408 may include, but is not limited to, a magnetic disk or an optical disk. Communication unit 409 allows electronic device 400 to exchange information / data with other devices via computer networks such as the Internet and / or various telecommunication networks and may include, but is not limited to, a modem, a network card, an infrared communication device, a wireless communication transceiver and / or a chipset, such as a Bluetooth™ device, a WiFi device, a WiMax device, a cellular communication device, and / or the like.

[0196] The computing unit 401 may be any general-purpose and / or specialized processing component with processing and computing capabilities. Some examples of the computing unit 401 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units that run machine learning model algorithms, a digital signal processor (DSP), and any appropriate processor, controller, microcontroller, etc. The computing unit 401 performs the various methods and processes described above. For example, in some embodiments, the aforementioned flexible DC converter station current harmonic suppression method may be implemented as a computer software program that is tangibly contained in a machine-readable medium, such as a storage unit 408. In some embodiments, part or all of the computer program may be loaded and / or installed on the electronic device 400 via the ROM 402 and / or the communication unit 409. In some embodiments, the computing unit 401 may be configured to execute the aforementioned flexible DC converter station current harmonic suppression method by any other appropriate means (e.g., by means of firmware).

[0197] The program code for implementing the method of the present invention can be written in any combination of one or more programming languages. Such program code can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device so that when the program code is executed by the processor or controller, the functions / operations specified in the flow chart and / or block diagram are implemented. The program code can be executed entirely on the machine, partially on the machine, as a stand-alone software package, partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0198] In the context of the present invention, machine-readable medium can be a tangible medium that can contain or store a program for use with an instruction execution system, device or equipment or used in combination with an instruction execution system, device or equipment. Machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared or semiconductor systems, devices or equipment, or any suitable combination of the foregoing. More specific examples of machine-readable storage media can include electrical connections based on one or more lines, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0199] As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, apparatus, and / or device (e.g., a magnetic disk, an optical disk, a memory, a programmable logic device (PLD)) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal used to provide machine instructions and / or data to a programmable processor.

[0200] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, voice input, or tactile input).

[0201] The systems and techniques described herein can be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include a local area network (LAN), a wide area network (WAN), and the Internet.

[0202] Computer systems may include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The client and server relationship arises through computer programs running on the respective computers and having a client-server relationship to each other.

[0203] It is obvious that those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without requiring creative effort. Therefore, the present invention is not limited to the above embodiments, and improvements and modifications made by those skilled in the art based on the disclosure of the present invention should fall within the scope of protection of the present invention.

Claims

1. A method for calculating sheath induced voltage and circulating current of a high-voltage AC submarine cable grounding system, characterized in that: include: The series impedance matrix and parallel admittance matrix of unit length high-voltage AC submarine cable without anchoring device and with anchoring device are constructed respectively; By using the series impedance matrix and the parallel admittance matrix, combined with the telegraph equation in the frequency domain, a series expansion is performed on the unit length high-voltage AC submarine cable in the double-end grounding mode to obtain the node admittance matrix of the unit length high-voltage AC submarine cable; The cascade formula of unit length HVAC submarine cables with and without intermediate grounding is derived, and the complete node admittance matrix of the HVAC submarine cable grounding system is obtained by combining the node admittance matrix of unit length HVAC submarine cables. Based on the voltage and current boundary conditions of the submarine cable and the complete node admittance matrix of the high-voltage AC submarine cable grounding system, a calculation model for the sheath induced voltage and circulating current of the high-voltage AC submarine cable grounding system with double-terminal grounding and anchoring device is constructed. The sheath induced voltage and circulating current are calculated based on the model.

2. The method for calculating sheath induced voltage and circulating current of a high-voltage AC submarine cable grounding system according to claim 1 is characterized in that: The construction process of the series impedance matrix and parallel admittance matrix of the unit length high-voltage AC submarine cable is as follows: Based on the geometric structure of the HVAC submarine cable grounding system and the material parameters of each dielectric layer, the structure of the anchoring device and its connection method with the HVAC submarine cable are analyzed, and the equivalent circuit of the anchoring device is obtained. Taking into account the electromagnetic coupling characteristics between the HVAC submarine cables and the influence of the grounding method of the HVAC submarine cable, the series impedance matrix and parallel admittance matrix per unit length of the HVAC submarine cable without and with the anchoring device are constructed respectively.

3. The method for calculating sheath induced voltage and circulating current of a high-voltage AC submarine cable grounding system according to claim 2, characterized in that: The specific construction process of the series impedance matrix of the unit length high-voltage AC submarine cable is as follows: Obtain the loop current matrix equation of a single-phase single-core high-voltage AC submarine cable without anchoring devices; The series impedance matrix of the single-phase single-core high-voltage AC submarine cable loop per unit length without anchoring device is obtained from the voltage and current telegraph equations of the single-phase single-core submarine cable per unit length and the current matrix equation of the single-phase single-core high-voltage AC submarine cable loop without anchoring device. The connection mode of the anchoring device and the equivalent circuit of the anchoring are analyzed to obtain the series impedance matrix of the unit length single-phase single-core high-voltage AC submarine cable including the anchoring device. The series impedance matrix of unit length single-phase single-core high-voltage AC submarine cable is extended to three-phase submarine cable. First, the calculation formula of the series impedance matrix of unit length high-voltage AC submarine cable without anchoring device is obtained, and then the calculation formula of the series impedance matrix of unit length high-voltage AC submarine cable with anchoring device is obtained.

4. The method for calculating sheath induced voltage and circulating current of a high-voltage AC submarine cable grounding system according to claim 2, characterized in that: The process of constructing the parallel admittance matrix of the unit length high-voltage AC submarine cable is as follows: Obtain the node voltage matrix equation of a single-phase single-core high-voltage AC submarine cable without anchoring devices; The parallel admittance matrix of the single-phase single-core high-voltage AC submarine cable per unit length without anchoring device is obtained from the voltage and current telegraph equations of the single-phase single-core submarine cable per unit length and the node voltage matrix equation of the single-phase single-core high-voltage AC submarine cable without anchoring device. The connection mode of the anchoring device and the equivalent circuit of the anchoring are analyzed to obtain the parallel admittance matrix of the unit length single-phase single-core high-voltage AC submarine cable including the anchoring device. The parallel admittance matrix of unit length single-phase single-core high-voltage AC submarine cable is extended to three-phase submarine cable. First, the calculation formula of the parallel admittance matrix of unit length high-voltage AC submarine cable without anchoring device is obtained, and then the calculation formula of the parallel admittance matrix of unit length high-voltage AC submarine cable with anchoring device is obtained.

5. The method for calculating sheath induced voltage and circulating current of a high-voltage AC submarine cable grounding system according to claim 2, characterized in that: The specific construction process of the node admittance matrix of the unit length high-voltage AC submarine cable is as follows: First, according to the telegraph equation in the frequency domain, the frequency domain equation of the transmission line is obtained: Among them, U x and I x They represent the voltage vector and current vector of the line conductor at point x in time t, Z is the series impedance matrix of the unit length high-voltage AC submarine cable, and Y is the parallel admittance matrix of the unit length high-voltage AC submarine cable; Then, according to the boundary conditions of voltage and current at the beginning and end of the submarine cable, we can get: Starting point, immediately x = 0 time, U x =U sd , I x =I sd ; At the end, that is, when x=l, U x =U md , I x =I md ; Substitute this into the differential equation to obtain: Among them, U sd and I sd are the voltage vector and current vector of the starting node of the submarine cable respectively; U md and I md are the voltage vector and current vector at the end node of the submarine cable respectively, where Γ is the propagation parameter, and the calculation expression is: Finally, by introducing the hyperbolic function through matrix transformation, the node admittance matrix of the unit length high-voltage AC submarine cable is obtained:

6. The method for calculating sheath induced voltage and circulating current of a high-voltage AC submarine cable grounding system according to claim 2, characterized in that: The derivation process of the cascade formula of the unit length high-voltage AC submarine cable with and without intermediate connection points is as follows: Combined with the node admittance matrix of the unit length HVAC submarine cable, the complete node admittance matrix of the HVAC submarine cable grounding system is obtained; First, for the admittance matrix Y without intermediate nodes a and Y b The specific formula is as follows: Among them, I S , I P ″ are Y a 、Y b The current at the head end of the corresponding submarine cable segment, I P ′、I R Y a 、Y b The current at the end of the corresponding submarine cable segment, U S 、U P ′ are Y a 、Y b The voltage matrix of the first end of the corresponding submarine cable to the ground, U P 、U R Y a 、Y b The voltage matrix of the end of the corresponding section of submarine cable to the ground, Y S 、Y m Y a 、Y b One quarter matrix of p Y a A quarter matrix of For two cascaded submarine cables, the currents flowing from both ends into their connection are equal in magnitude and opposite in direction, and the relationship is: I′ P +I′ P ′=0, The cascade formula of the admittance matrix without intermediate nodes is obtained: Then, for a cascade with an intermediate ground node, the specific formula is: Among them, Y1′ and Y2′ are the admittance matrices including the intermediate ground nodes, and E ij 、F ij , G ij 、H ij They are the submatrices of the quarter node admittance matrix E, F, G, and H of Y1′, representing the intermediate matrix in the node admittance matrix, i, j = 1, 2; Q ij 、W ij 、S ij 、R ij are the submatrices of the quarter node admittance matrix Q, W, S, and R of Y2′, representing the intermediate matrix in the node admittance matrix; E 11 、F 11 , G 11 、H 11 , Q 11 、W 11 、S 11 、R 11 The order of E is (n-1)×(n-1); 12 、F 12 , G 12 、H 12 , Q 12 、W 12 、S 12 、R 12 The order of E is (n-1)×1; 21 、F 21 , G 21 、H 21 , Q 21 、W 21 、S 21 、R 21 The order of E is 1×(n-1); 22 、F 22 , G 22 、H 22 , Q 22 、W 22 、S 22 、R 22 The order is 1×1, and n is the number of submarine cables; in, a=S、P or R For the admittance matrices Y1′ and Y2′ containing the intermediate ground node, the admittance matrix after the cascade of the admittance matrices of the Y1′ and Y2′ nodes is obtained: Where T1 and T2 are Y′ 12 The intermediate matrix of is expressed as follows: T1=(H 11 +Q 11 ) -1 G 11 , T2=(H 11 +Q 11 ) -1 W 11 , At this point, the node admittance matrices with and without intermediate locations are constructed by the cascade algorithm.

7. The method for calculating sheath voltage and loop current of a high-voltage AC submarine cable grounding system according to claim 1, characterized in that: The construction process of the sheath induced voltage and circulating current calculation model of the high-voltage AC submarine cable grounding system taking into account the anchor device under the double-end grounding method is as follows: First, perform matrix transformation on the voltage and current values at the sending and receiving ends of the jth section of the i-th section of the high-voltage AC submarine cable, and obtain the following calculation formula: Among them, Y S,i,j 、Y R,i,j is a symmetric quarter matrix, i=1,2,3; U S,i,j is the voltage at the sending end of the jth section of the i-th high-voltage AC submarine cable; U R,i,j is the voltage at the receiving end of the jth section of the i-th section of high-voltage AC submarine cable; I S,i,j is the current at the sending end of the jth section of the i-th section of high-voltage AC submarine cable; I R,i,j is the current at the receiving end of the jth section of the i-th section of high-voltage AC submarine cable; Secondly, the above formula is used to calculate the cable section containing the anchoring device to obtain the voltage and current U of the jth receiving end of the i-th high-voltage AC submarine cable. R,i,j , I R,i,j , and then use the following formula to calculate the sheath induced voltage and circulating current of the remaining submarine cable sections without anchoring devices: Where, I R ″ ,i,j 、U R ″ ,i.j They represent the calculated induced voltage and circulating current of the submarine cable section without anchoring devices; According to the induced voltage and circulating current, the sheath induced voltage and circulating current of the high-voltage AC submarine cable grounding system are derived using a cascade algorithm.

8. A sheath induced voltage and circulating current calculation system for a high-voltage AC submarine cable grounding system, characterized in that: include: Matrix construction unit: constructs the series impedance matrix and parallel admittance matrix of the unit length high-voltage AC submarine cable without anchoring devices and with anchoring devices respectively; A node admittance matrix acquisition unit is configured to perform series expansion on a unit length high-voltage AC submarine cable in a double-end grounding mode by utilizing the series impedance matrix and the parallel admittance matrix in combination with the frequency domain telegraph equation to obtain the node admittance matrix of the unit length high-voltage AC submarine cable. Complete node admittance matrix acquisition unit: derives the cascade formula of unit-length submarine cables with and without intermediate grounding points, and combines the node admittance matrix of unit-length high-voltage AC submarine cables to obtain the complete node admittance matrix of the high-voltage AC submarine cable grounding system; Induced voltage and circulating current calculation unit: Based on the voltage and current boundary conditions of the submarine cable and the complete node admittance matrix of the high-voltage AC submarine cable grounding system, a sheath induced voltage and circulating current calculation model for the high-voltage AC submarine cable grounding system under double-terminal grounding mode and including the anchor device is constructed, and the sheath induced voltage and circulating current are calculated based on the said model.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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