Cable sequence shunt capacitance calculation method

Abstract

The invention discloses a cable sequence shunt capacitance calculation method. The method comprises the following steps: (1) constructing a cable full-dimensional shunt capacitance matrix; (2) calculating elements in the full-dimensional shunt capacitance matrix of the cable; (3) calculating a cable phase shunt capacitance matrix according to the cable full-dimensional shunt capacitance matrix in combination with a cable connection mode and a grounding mode; and (4) according to the cable phase shunt capacitor matrix, calculating a sequence shunt capacitor matrix through phase sequence conversion, wherein diagonal elements of the sequence shunt capacitor matrix are sequence shunt capacitors. According to the invention, cable structure differences are fully considered, and capacitive coupling among conductor layers of a single-core cable with an armor layer, a single-core cable without an armor layer and a three-core cable is analyzed; according to the method, the difference between a cable connection mode and a grounding mode is fully considered, the influence of fixed connection, single-point connection and cross connection on capacitance distribution is analyzed, the comprehensiveness of cable sequence shunt capacitance calculation is greatly improved, most of cables with different structures and connection modes can be covered, and the method has a good application effect in practical engineering.

Description

Technical Field

[0001] The present invention belongs to the technical field of power transmission and distribution of electric power systems, and in particular relates to a method for calculating the sequence shunt capacitance of a cable. Background Art

[0002] Cables are key components in the transmission and distribution of power systems. Underground cables are widely used in urban power systems due to their compact footprint and high reliability. Submarine cables are used to transmit power between islands and the mainland, and their use is expected to increase significantly with the development of offshore wind power. However, cables exhibit significant capacitance, which, if not properly coordinated with the inductive components in the system, can lead to resonant stability issues. Therefore, accurately calculating the cable's sequence shunt capacitance is crucial for power system planning and design, resonant stability analysis, and fault diagnosis.

[0003] At present, some progress has been made in the calculation method of cable sequence shunt capacitance. For example, the literature [Xu Zheng, Li Sixun, Jin Yanqiu. Calculation of electrical parameters of submarine cables in harmonic frequency bands [J]. Automation of Electric Power Systems, 2021, 45(21):76-84.] only uses the shunt capacitance between the core layer and the sheath layer as the sequence shunt capacitance, failing to fully consider the differences in cable structure. The literature [Xu Zheng, Qian Jie. Different calculation methods for cable electrical parameters and their comparison [J]. High Voltage Technology, 2013, 39(3):689-697.] introduces the formula for calculating the cable sequence shunt capacitance using the built-in power_cableparam function in MATLAB. This formula can only be used to calculate cables with equal spacing. This formula is not applicable to cables with non-equal spacing or those with armored layers.

[0004] It can be seen that there are some deficiencies in the calculation method of cable sequence parallel capacitance in the existing technology, especially in terms of comprehensiveness: on the one hand, different cables have significant differences in structure. Single-core cables usually include a core layer, a sheath layer and an armor layer, and there is no capacitive coupling between different phases, while three-core cables involve phase-to-phase capacitive coupling and a complex capacitive coupling relationship between the sheath layer and the armor layer; on the other hand, the connection method and grounding method of the cable have a significant impact on the parallel capacitance. Different connection methods (such as fixed connection, single-point connection and cross connection) will lead to different capacitance distributions; if the method fails to fully consider the differences in cable structure, as well as the differences in connection method and grounding method, it will limit its application effect in actual engineering, especially in scenarios with complex cable structures and diversified connection methods. Summary of the Invention

[0005] In view of the above, the present invention provides a method for calculating the sequence parallel capacitance of a cable, which can solve the problems of the traditional method of obtaining the electrical parameters of submarine cables, such as lack of specificity and accuracy.

[0006] A method for calculating cable sequence parallel capacitance, comprising:

[0007] Construct a full-dimensional parallel capacitance matrix of the cable; calculate and determine the element values ​​in the full-dimensional parallel capacitance matrix based on the cable structural parameters, including the parallel capacitance between the cable core layer and the sheath layer, the parallel capacitance between the sheath layer and the armor layer of a single-core cable, the parallel capacitance between the cable armor layer and the earth or seawater, the parallel capacitance between the sheath layer of a single-core cable and the earth or seawater, the parallel capacitance between the sheath layers of a three-core cable, and the parallel capacitance between the sheath layer and the armor layer of a three-core cable;

[0008] Calculate the phase parallel capacitance matrix of the cable based on the element values ​​in the full-dimensional parallel capacitance matrix combined with the cable connection method and grounding method;

[0009] The sequence shunt capacitance matrix of the cable is calculated based on the phase shunt capacitance matrix, and its diagonal elements are the sequence shunt capacitances.

[0010] Furthermore, for a single-core cable with an armored layer, the expression of its full-dimensional parallel capacitance matrix is ​​as follows:

[0011]

[0012] Furthermore, for a single-core cable without an armor layer, the expression of its full-dimensional parallel capacitance matrix is ​​as follows:

[0013]

[0014] Where: Capacitor element C imin It represents the parallel capacitance between conductor layer m and conductor layer n of phase i cable. Subscript i is the phase identifier, i=A, B, C corresponds to phase ABC of cable. Subscript m and n are the conductor layer identifiers, m, n=c, s, a, c represents the core layer, s represents the sheath layer, and a represents the armor layer. Capacitance element C imE represents the parallel capacitance between the conductor layer m of the i-phase cable and the earth or seawater, where the subscript E represents the earth or seawater; C Full represents the full-dimensional parallel capacitance matrix, C cc represents the diagonal capacitance matrix with the core self-capacitance as the diagonal element; C cs represents the diagonal capacitance matrix with the mutual capacitance between the core layer and the sheath layer as the diagonal element; C ca represents the diagonal capacitance matrix with the mutual capacitance between the core layer and the armor layer as the diagonal element; C ss represents the diagonal capacitance matrix with the sheath layer self-capacitance as the diagonal element; C sa represents the diagonal capacitance matrix with the mutual capacitance between the sheath layer and the armor layer as the diagonal element; C aa represents the diagonal capacitance matrix with the armor layer self-capacitance as the diagonal element; C csa Indicated by Ccs and C ca The capacitor matrix composed of ssaa Indicated by C ss 、C sa and C aa The capacitor matrix is ​​composed of T Indicates transpose.

[0015] Furthermore, for a three-core cable, the expression of its full-dimensional parallel capacitance matrix is ​​as follows:

[0016]

[0017] Where: Capacitor element C imjn It represents the parallel capacitance between the conductor layer m of the i-phase cable and the conductor layer n of the j-phase cable. The subscripts i and j are phase identifiers, i, j = A, B, C, 0 corresponds to the ABC phases of the cable and no phase; the subscripts m and n are conductor layer identifiers, m, n = c, s, a, c represents the core layer, s represents the sheath layer, and a represents the armor layer; the capacitance element C imE represents the parallel capacitance between the conductor layer m of the i-phase cable and the earth or seawater, where the subscript E represents the earth or seawater; C Full represents the full-dimensional parallel capacitance matrix, C cc represents the diagonal capacitance matrix with the core self-capacitance as the diagonal element; C cs represents the diagonal capacitance matrix with the mutual capacitance between the core layer and the sheath layer as the diagonal element; C ca represents the diagonal capacitance matrix with the mutual capacitance between the core layer and the armor layer as the diagonal element; C ss represents the diagonal capacitance matrix with the self-capacitance of the sheath layer as the diagonal element and the mutual capacitance between the sheath layers as the non-diagonal element; C sa represents a column vector with the mutual capacitance between the sheath layer and the armor layer as its elements; C aa Indicates the self-capacitance of the armor layer; C csa Indicated by C cs and C ca The capacitor matrix composed of ssaa Indicated by C ss 、C sa and C aa The capacitor matrix is ​​composed of T Indicates transpose.

[0018] Furthermore, the calculation expression for the parallel capacitance between the cable core layer and the sheath layer is as follows:

[0019]

[0020] Where: C icis Represents the parallel capacitance between the core layer and sheath layer of the i-phase cable, ε icsRepresents the relative dielectric constant of the insulating material between the core layer and the sheath layer of the i-phase cable, r i_is Indicates the inner radius of the i-phase cable sheath, r o_ic Indicates the outer radius of the i-phase cable core layer.

[0021] Furthermore, the calculation expression for the parallel capacitance between the cable armor layer and the earth or seawater is as follows:

[0022]

[0023] Where: C iaE Represents the parallel capacitance between the i-phase cable armor layer and the earth or seawater, ε iaE Represents the relative dielectric constant of the insulating material between the i-phase cable armor layer and the earth or seawater, r o_ia Indicates the outer radius of the armor layer of phase i cable, t ips_a Indicates the thickness of the insulation layer between the i-phase cable armor and the earth or seawater.

[0024] Furthermore, the calculation expression for the parallel capacitance between the sheath layer of a single-core cable and the earth or seawater is as follows:

[0025]

[0026] Where: C isE Represents the parallel capacitance between the i-phase cable sheath and the earth or seawater, ε isE Represents the relative dielectric constant of the insulating material between the i-phase cable sheath and the earth or seawater, r o_is Indicates the outer radius of the i-phase cable sheath, t ips_s Indicates the thickness of the insulation layer between the i-phase cable sheath and the earth or seawater.

[0027] Furthermore, for the parallel capacitance between the sheath layers of a three-core cable, the calculation expression is as follows:

[0028]

[0029] Where: C isjs Represents the parallel capacitance between the i-phase cable sheath layer and the j-phase cable sheath layer, ε 0sa Represents the relative dielectric constant of the insulating material between the sheath layer and the armor layer, r i_0a Indicates the inner radius of the armor layer, r o_is Indicates the outer radius of the i-phase cable sheath.

[0030] Furthermore, the calculation expression for the parallel capacitance between the sheath layer and the armor layer of a single-core cable is as follows:

[0031]

[0032] Where: C isia Represents the parallel capacitance between the i-phase cable sheath and armor layer, ε isa Represents the relative dielectric constant of the insulating material between the i-phase cable sheath and armor layer, r i_ia Indicates the inner radius of the armor layer of phase i cable, r o_is Indicates the outer radius of the i-phase cable sheath.

[0033] Furthermore, the calculation expression for the parallel capacitance between the sheath layer and the armor layer of a three-core cable is as follows:

[0034]

[0035] Where: C is0a Represents the parallel capacitance between the i-phase cable sheath and armor layer, ε 0sa Represents the relative dielectric constant of the insulating material between the sheath layer and the armor layer, r i_0a Indicates the inner radius of the armor layer, r o_is Represents the outer radius of the i-phase cable sheath, r o ic Indicates the outer radius of the i-phase cable core layer.

[0036] Furthermore, for a single-core cable or a three-core cable with a fixed connection, the calculation expression of the phase parallel capacitance matrix is ​​as follows:

[0037] C Phase =C cc

[0038] For a single-core cable with an armored layer connected at a single point, the calculation expression for the parallel capacitance matrix is ​​as follows:

[0039]

[0040] For a single-core cable without armor layer using a single-point connection method, the calculation expression of its phase parallel capacitance matrix is ​​as follows:

[0041]

[0042] For a single-core cable with a cross-connection method, the calculation expression of its phase parallel capacitance matrix is ​​as follows:

[0043] C Phase =C cc_new

[0044] Where: C Phase Represents the phase parallel capacitance matrix, C cc_new is a diagonal capacitance matrix with equal diagonal elements, and its diagonal elements are C cc Mean of the diagonal elements.

[0045] Furthermore, the calculation expression of the sequential parallel capacitance matrix is ​​as follows:

[0046]

[0047] Where: C ZPN Represents the sequence parallel capacitance matrix, the elements on the diagonal from top to bottom are zero sequence parallel capacitance, positive sequence parallel capacitance, negative sequence parallel capacitance, C Phase represents the phase parallel capacitance matrix, A is the phase sequence transformation matrix, a is a complex operator and a=e j120° , e is a natural constant, and j is an imaginary unit.

[0048] In a second aspect, the present invention provides a cable sequence parallel capacitance calculation system, comprising:

[0049] A full-dimensional matrix construction unit, used to construct a full-dimensional parallel capacitance matrix of the cable;

[0050] A matrix element calculation unit, used for calculating and determining element values ​​in a full-dimensional parallel capacitance matrix according to cable structural parameters;

[0051] A capacitance matrix calculation unit is used to calculate the phase parallel capacitance matrix of the cable according to the element values ​​in the full-dimensional parallel capacitance matrix combined with the cable connection mode and the grounding mode;

[0052] The sequence parallel capacitance calculation unit is used to calculate the sequence parallel capacitance matrix of the cable according to the phase parallel capacitance matrix, wherein the diagonal elements are the sequence parallel capacitances.

[0053] In a third aspect, the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and the processor is configured to execute the computer program to implement the above-mentioned cable sequence parallel capacitance calculation method.

[0054] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program, which is used to implement the above-mentioned cable sequence parallel capacitance calculation method when executed by a processor.

[0055] Compared with existing methods, the present invention has the advantage of fully accounting for differences in cable structure, analyzing the capacitive coupling between the conductor layers of armored single-core cables, unarmored single-core cables, and three-core cables. It also fully considers differences in cable connection and grounding methods, analyzing the effects of fixed connections, single-point connections, and cross-connections on capacitance distribution. Consequently, the present invention significantly improves the comprehensiveness of cable sequence parallel capacitance calculations, covering the vast majority of cables with different structures and connection methods, and has demonstrated excellent application results in practical engineering projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 Schematic diagram of the flow of the cable sequence parallel capacitance calculation method of the present invention;

[0057] Figure 2 It is a schematic diagram of the structure of a single-core cable with an armored layer;

[0058] Figure 3 This is a schematic diagram of the structure of a single-core cable without an armor layer;

[0059] Figure 4 It is a structural diagram of a three-core cable;

[0060] Figure 5 This is a schematic diagram of the structure of a single-phase coupled parallel capacitor circuit for a single-core cable with an armored layer;

[0061] Figure 6 This is a schematic diagram of the circuit structure of a single-phase coupled parallel capacitor for a single-core cable without an armor layer;

[0062] Figure 7 Schematic diagram of the coupled parallel capacitor circuit structure of a three-core cable;

[0063] Figure 8 Schematic diagram of the fixed connection method of the cable;

[0064] Figure 9 Schematic diagram of single-point connection of cable;

[0065] Figure 10 Schematic diagram of the cross-connection method of cables;

[0066] Figure 11 A schematic diagram showing the comparison of the positive-sequence and zero-sequence π-model parallel susceptance lumped parameters in the cable calculation example of the present invention;

[0067] Figure 12 The figure is a schematic diagram of the structure of an electronic device implemented according to the method of the present invention. DETAILED DESCRIPTION

[0068] In order to describe the present invention more specifically, the technical solution of the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0069] like Figure 1 As shown, the cable sequence parallel capacitance calculation method of the present invention includes the following steps:

[0070] (1) Construct the full-dimensional parallel capacitance matrix of the cable, including the full-dimensional parallel capacitance matrix of the single-core cable and the three-core cable.

[0071] The structure of single-core cable with armor layer is as follows Figure 2 As shown, its single-phase coupled parallel capacitor circuit is as follows Figure 5 As shown, the corresponding full-dimensional parallel capacitance matrix expression is as follows:

[0072]

[0073] Where: Capacitor element C imin It represents the parallel capacitance between conductor layer m and conductor layer n of phase i. Subscript i is the phase identifier, i=A, B, C corresponds to the ABC phase of the cable, subscript m, n are the conductor layer identifiers, m, n=c, s, a, c represents the core layer, s represents the sheath layer, and a represents the armor layer; the capacitance element C imE represents the parallel capacitance between the conductor layer m of phase i and the earth / seawater, E represents the earth / seawater; C Full represents the full-dimensional parallel capacitance matrix; C cc represents the diagonal capacitance matrix with the core self-capacitance as the diagonal element; C cs represents the diagonal capacitance matrix with the mutual capacitance between the core layer and the sheath layer as the diagonal element; C ca represents the diagonal capacitance matrix with the mutual capacitance between the core layer and the armor layer as the diagonal element; C ss represents the diagonal capacitance matrix with the sheath layer self-capacitance as the diagonal element; C sa represents the diagonal capacitance matrix with the mutual capacitance between the sheath layer and the armor layer as the diagonal element; C aa represents the diagonal capacitance matrix with the armor layer self-capacitance as the diagonal element; C csa Indicates C cs and C ca The capacitor matrix composed of C ssaa Indicates C ss 、C sa and C aa The capacitor matrix.

[0074] The structure of single-core cable without armor layer is as follows Figure 3 As shown, its single-phase coupled parallel capacitor circuit is as follows Figure 6 As shown, the corresponding full-dimensional parallel capacitance matrix expression is as follows:

[0075]

[0076] The structure of three-core cable is as follows Figure 4 As shown, its coupled parallel capacitor circuit is as follows Figure 7 As shown, the corresponding full-dimensional parallel capacitance matrix expression is as follows:

[0077]

[0078] Where: Capacitor element C imjnIt represents the parallel capacitance between the conductor layer m of phase i and the conductor layer n of phase j. The subscripts i and j are phase identifiers. i, j = A, B, C, 0 corresponds to the ABC phases and no phase of the cable. The subscripts m and n are conductor layer identifiers. m, n = c, s, a, c represents the core layer, s represents the sheath layer, and a represents the armor layer. The capacitance element C imE represents the parallel capacitance between the conductor layer m of phase i and the earth / seawater, E represents the earth / seawater; C Full represents the full-dimensional parallel capacitance matrix; C cc represents the diagonal capacitance matrix with the core self-capacitance as the diagonal element; C cs represents the diagonal capacitance matrix with the mutual capacitance between the core layer and the sheath layer as the diagonal element; C ca represents the diagonal capacitance matrix with the mutual capacitance between the core layer and the armor layer as the diagonal element; C ss represents a symmetric capacitance matrix with the sheath layer self-capacitance as the diagonal element and the mutual capacitance between the sheath layers as the non-diagonal element; C sa represents a column vector with mutual capacitance between the sheath layer and the armor layer as its elements; C aa Represents the armor layer self-capacitance; C csa Indicates C cs and C ca The capacitor matrix composed of C ssaa Indicates C ss 、C sa and C aa The capacitor matrix.

[0079] (2) Calculate the elements in the full-dimensional parallel capacitance matrix of the cable based on the cable structural parameters, including the parallel capacitance between the core layer and the sheath layer, the parallel capacitance between the sheath layer and the armor layer, and the parallel capacitance between the sheath layer / armor layer and the earth / seawater of a single-core cable; the parallel capacitance between the core layer and the sheath layer, the parallel capacitance between the sheath layer and the sheath layer, the parallel capacitance between the sheath layer and the armor layer, and the parallel capacitance between the armor layer and the earth / seawater of a three-core cable;

[0080] The calculation expressions for the parallel capacitance between the core layer and the sheath layer of a single-core cable and the parallel capacitance between the core layer and the sheath layer of a three-core cable are as follows:

[0081]

[0082] Where: C icis Represents the parallel capacitance between the core layer and the sheath layer of phase i, in μF / km, where the subscript i is the phase identifier, i=A, B, C corresponds to the ABC phases of the cable; ε ics Represents the relative dielectric constant of the insulation material between the core layer and the sheath layer of phase i; r i_is Indicates the inner radius of the i-phase sheath layer, in mm; r o_ic Indicates the outer radius of the core layer of phase i, in mm.

[0083] The calculation expression of the parallel capacitance between the sheath layer and the armor layer of a single-core cable with an armor layer is as follows:

[0084]

[0085] Where: C isia Represents the parallel capacitance between the sheath layer and the armor layer of phase i, in μF / km, where the subscript i is the phase identifier, i=A, B, C corresponds to the ABC phases of the cable; ε isa Represents the relative dielectric constant of the insulating material between the i-phase sheath layer and the armor layer; r i_ia Indicates the inner radius of the armor layer of phase i, in mm; r o_is Indicates the outer radius of the i-phase sheath layer, in mm.

[0086] The calculation expressions for the parallel capacitance between the armor layer of a single-core cable with an armor layer and the earth / seawater, and the parallel capacitance between the armor layer of a three-core cable and the earth / seawater are as follows:

[0087]

[0088] Where: C iaE Represents the parallel capacitance between the armor layer of phase i and the earth / seawater, in μF / km, with the subscript i being the phase identifier, i=A, B, C, and 0 corresponding to the ABC phases of the cable and no phase; ε iaE Represents the relative dielectric constant of the insulating material between the i-phase armor layer and the earth / seawater; r o_ia Indicates the outer radius of the armor layer of phase i, in mm; t ips_a Indicates the thickness of the insulation layer between the i-phase armor layer and the earth / seawater, in mm.

[0089] The calculation expression for the parallel capacitance between the sheath layer of a single-core cable without an armor layer and the earth / seawater is as follows:

[0090]

[0091] Where: C isE Represents the parallel capacitance between the i-phase sheath layer and the earth / seawater, in μF / km, where the subscript i is the phase identifier, i=A, B, C corresponds to the ABC phases of the cable; ε isE Represents the relative dielectric constant of the insulating material between the i-phase sheath layer and the earth / seawater; r o_is Indicates the outer radius of the i-phase sheath layer, in mm; t ips_s Indicates the thickness of the insulation layer between the i-phase sheath and the earth / seawater, in mm.

[0092] The calculation expression of the parallel capacitance between the sheath layers of a three-core cable is as follows:

[0093]

[0094] Where: C isjs It represents the parallel capacitance between the sheath layer of phase i and the sheath layer of phase j, in μF / km. The subscripts i and j are phase identifiers, i, j = A, B, C correspond to the ABC phases of the cable; ε 0sa Represents the relative dielectric constant of the insulating material between the sheath layer and the armor layer; r i_0a Indicates the inner radius of the armor layer, in mm; r o_is Indicates the outer radius of the i-phase sheath layer, in mm.

[0095] The calculation expression of the parallel capacitance between the sheath layer and the armor layer of a three-core cable is as follows:

[0096]

[0097] Where: C is0a Represents the parallel capacitance between the sheath layer and the armor layer of phase i, in μF / km, where the subscript i is the phase identifier, i=A, B, C corresponds to the ABC phases of the cable; ε 0sa Represents the relative dielectric constant of the insulating material between the sheath layer and the armor layer; r i_0a Indicates the inner radius of the armor layer, in mm; r o_is Indicates the outer radius of the i-phase sheath layer, in mm; r o_ic Indicates the outer radius of the core layer of phase i, in mm.

[0098] (3) Based on the full-dimensional parallel capacitance matrix of the cable obtained in steps (1) and (2), combined with the cable connection method and grounding method, calculate the cable phase parallel capacitance matrix.

[0099] Use Figure 8 The calculation expressions for the single-core cable phase parallel capacitance matrix and the three-core cable phase parallel capacitance matrix of the fixed connection mode shown are as follows:

[0100] C Phase =C cc

[0101] Where: C Phase represents the phase parallel capacitance matrix.

[0102] Use Figure 9 The calculation expression of the parallel capacitance matrix of the single-core cable with armor layer in the single-point connection mode shown is as follows:

[0103]

[0104] Use Figure 9 The calculation expression of the parallel capacitance matrix of the single-core cable without armor layer in the single-point connection mode shown is as follows:

[0105]

[0106] Use Figure 10 The calculation expression of the parallel capacitance matrix of the single-core cable in the cross-connection mode shown is as follows:

[0107] C Phase =C cc_new

[0108] Where: C cc_new is a diagonal capacitance matrix with equal diagonal elements, and its diagonal elements are C cc Mean of the diagonal elements.

[0109] (4) Based on the cable phase shunt capacitance matrix obtained in step (3), calculate the cable sequence shunt capacitance matrix, whose diagonal elements are the sequence shunt capacitances.

[0110] The cable sequence parallel capacitance matrix is ​​obtained by phase sequence transformation. The transformation process is as follows:

[0111]

[0112] Where: C ZPN represents the sequence shunt capacitor matrix, the elements on the diagonal from top to bottom are zero sequence shunt capacitor, positive sequence shunt capacitor, negative sequence shunt capacitor; A is the phase sequence transformation matrix, the complex operator a = e j120° .

[0113] Below, we take a single-core submarine cable as an example and calculate the parallel susceptance lumped parameters in the positive-sequence and zero-sequence π models from 1 to 2000 Hz based on the sequence parallel capacitance calculated by the method of the present invention. To verify the accuracy of the method of the present invention, the widely accepted electromagnetic transient simulation software PSCAD is used for comparison. The submarine cable parameters of the single-core cable are shown in Table 1:

[0114] Table 1

[0115]

[0116] from Figure 11 The comparison results show that the parallel susceptance lumped parameters in the positive-sequence and zero-sequence π models calculated by the method of the present invention are basically consistent with the PSCAD sweep frequency test results, indicating that the method of the present invention is reliable and can be applied to actual engineering calculations.

[0117] An embodiment of the present invention further provides a cable sequence parallel capacitance calculation system, comprising: a full-dimensional matrix construction unit, a matrix element calculation unit, a capacitance matrix calculation unit, and a sequence parallel capacitance calculation unit;

[0118] The full-dimensional matrix construction unit is used to construct the full-dimensional parallel capacitance matrix of the cable;

[0119] For a single-core cable with an armored layer, the expression of its full-dimensional parallel capacitance matrix is ​​as follows:

[0120]

[0121] For a single-core cable without armor, the expression of its full-dimensional parallel capacitance matrix is ​​as follows:

[0122]

[0123] For a three-core cable, the expression of its full-dimensional parallel capacitance matrix is ​​as follows:

[0124]

[0125] The matrix element calculation unit is used to calculate and determine the element values ​​in the full-dimensional parallel capacitance matrix according to the cable structural parameters;

[0126] The calculation expression for the parallel capacitance between the cable core layer and the sheath layer is as follows:

[0127]

[0128] The calculation expression for the parallel capacitance between the cable armor layer and the earth or seawater is as follows:

[0129]

[0130] The calculation expression for the parallel capacitance between the sheath layer of a single-core cable and the earth or seawater is as follows:

[0131]

[0132] For the parallel capacitance between the sheath layers of a three-core cable, the calculation expression is as follows:

[0133]

[0134] For the parallel capacitance between the sheath and armor of a single-core cable, the calculation expression is as follows:

[0135]

[0136] The calculation expression for the parallel capacitance between the sheath layer and the armor layer of a three-core cable is as follows:

[0137]

[0138] The capacitance matrix calculation unit is used to calculate the phase parallel capacitance matrix of the cable according to the element values ​​in the full-dimensional parallel capacitance matrix combined with the cable connection method and the grounding method;

[0139] For single-core cables or three-core cables with fixed connections, the calculation expression of the phase parallel capacitance matrix is ​​as follows:

[0140] C Phase =C cc

[0141] For a single-core cable with an armored layer connected at a single point, the calculation expression for the parallel capacitance matrix is ​​as follows:

[0142]

[0143] For a single-core cable without armor layer using a single-point connection method, the calculation expression of its phase parallel capacitance matrix is ​​as follows:

[0144]

[0145] For a single-core cable with a cross-connection method, the calculation expression of its phase parallel capacitance matrix is ​​as follows:

[0146] C Phase =C cc_new

[0147] The sequence parallel capacitance calculation unit is used to calculate the sequence parallel capacitance matrix of the cable based on the phase parallel capacitance matrix. Its diagonal elements are the sequence parallel capacitances. The calculation expression of the sequence parallel capacitance matrix is ​​as follows:

[0148]

[0149] Accordingly, the present invention also provides an electronic device, comprising a processor and a memory, wherein the memory is used to store a computer program, and the processor is used to execute the computer program to implement the above-mentioned cable sequence parallel capacitance calculation method. Figure 12 The figure shows a hardware structure of any electronic device with data processing capability where the cable parallel capacitance calculation system provided by the embodiment of the present invention is located. Figure 12 In addition to the processor, memory, and network interface shown, the electronic device with data processing capabilities in which the system is located in the embodiment may also include other hardware according to the actual functions of the electronic device, which will not be described in detail.

[0150] Accordingly, the present invention also provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the cable sequence parallel capacitance calculation method as described above. The computer-readable storage medium can be an internal storage unit of the aforementioned electronic device with data processing capabilities, such as a hard disk or memory; or it can be other external storage devices, such as a plug-in hard disk, smart memory card (Smart Media Card, SMC), SD card, flash card (Flash Card), etc. equipped on the device. The computer-readable storage medium can also include both an internal storage unit of an electronic device with data processing capabilities and an external storage device, for storing the computer program and other programs and data required by the electronic device with data processing capabilities, and can also be used to temporarily store data that has been output or is to be output.

[0151] The above description of the embodiments is intended to facilitate understanding and application of the present invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to the above embodiments and apply the general principles described herein to other cases without requiring creative effort. Therefore, the present invention is not limited to the above embodiments, and improvements and modifications made to the present invention 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 cable sequence parallel capacitance, comprising: Construct the full-dimensional parallel capacitance matrix of the cable; Calculate and determine the element values ​​in the full-dimensional parallel capacitance matrix based on the cable structural parameters; Calculate the phase parallel capacitance matrix of the cable based on the element values ​​in the full-dimensional parallel capacitance matrix combined with the cable connection method and grounding method; The sequence parallel capacitance matrix of the cable is calculated according to the phase parallel capacitance matrix, and the diagonal elements in the sequence parallel capacitance matrix are used as the sequence parallel capacitances.

2. The method for calculating cable sequence parallel capacitance according to claim 1, wherein: The cables include single-core cables with and without armor layers. The expression of the full-dimensional parallel capacitance matrix of the single-core cable with armor layers is as follows: The expression of the full-dimensional parallel capacitance matrix of a single-core cable without armor layer is as follows: Where: Capacitor element C imin It represents the parallel capacitance between conductor layer m and conductor layer n of phase i cable. Subscript i is the phase identifier, i=A, B, C corresponds to phase ABC of cable. Subscript m and n are the conductor layer identifiers, m, n=c, s, a, c represents the core layer, s represents the sheath layer, and a represents the armor layer. Capacitance element C imE represents the parallel capacitance between the conductor layer m of the i-phase cable and the earth or seawater, where the subscript E represents the earth or seawater; C Full represents the full-dimensional parallel capacitance matrix, C cc represents the diagonal capacitance matrix with the core self-capacitance as the diagonal element; C cs represents the diagonal capacitance matrix with the mutual capacitance between the core layer and the sheath layer as the diagonal element; C ca represents the diagonal capacitance matrix with the mutual capacitance between the core layer and the armor layer as the diagonal element; C ss represents the diagonal capacitance matrix with the sheath layer self-capacitance as the diagonal element; C sa represents the diagonal capacitance matrix with the mutual capacitance between the sheath layer and the armor layer as the diagonal element; C aa represents the diagonal capacitance matrix with the armor layer self-capacitance as the diagonal element; C csa Indicated by C cs and C ca The capacitor matrix composed of ssaa Indicated by C ss 、C sa and C aa The capacitance matrix composed of , T represents the transpose.

3. The method for calculating cable sequence parallel capacitance according to claim 1, wherein: The cable includes a three-core cable, and the expression of the full-dimensional parallel capacitance matrix of the three-core cable is as follows: Where: Capacitor element C imjn It represents the parallel capacitance between the conductor layer m of the i-phase cable and the conductor layer n of the j-phase cable. The subscripts i and j are phase identifiers, i, j = A, B, C, 0 corresponds to the ABC phases of the cable and no phase; the subscripts m and n are conductor layer identifiers, m, n = c, s, a, c represents the core layer, s represents the sheath layer, and a represents the armor layer; the capacitance element C imE represents the parallel capacitance between the conductor layer m of the i-phase cable and the earth or seawater, where the subscript E represents the earth or seawater; C Full represents the full-dimensional parallel capacitance matrix, C cc represents the diagonal capacitance matrix with the core self-capacitance as the diagonal element; C cs represents the diagonal capacitance matrix with the mutual capacitance between the core layer and the sheath layer as the diagonal element; C ca represents the diagonal capacitance matrix with the mutual capacitance between the core layer and the armor layer as the diagonal element; C ss represents the diagonal capacitance matrix with the self-capacitance of the sheath layer as the diagonal element and the mutual capacitance between the sheath layers as the non-diagonal element; C sa represents a column vector with the mutual capacitance between the sheath layer and the armor layer as its elements; C aa Indicates the self-capacitance of the armor layer; C csa Indicated by C cs and C ca The capacitor matrix composed of C ssaa Indicated by C ss 、C sa and C aa The capacitance matrix composed of , T represents the transpose.

4. The method for calculating cable sequence parallel capacitance according to claim 1, wherein: The calculation expression for the parallel capacitance between the cable core layer and the sheath layer is as follows: Where: C icis Represents the parallel capacitance between the core layer and sheath layer of the i-phase cable, ε ics Represents the relative dielectric constant of the insulating material between the core layer and the sheath layer of the i-phase cable, r i_is Indicates the inner radius of the i-phase cable sheath, r o_ic Indicates the outer radius of the i-phase cable core layer.

5. The method for calculating cable sequence parallel capacitance according to claim 1, wherein: The calculation expression for the parallel capacitance between the cable armor layer and the earth or seawater is as follows: Where: C iaE Represents the parallel capacitance between the i-phase cable armor layer and the earth or seawater, ε iaE Represents the relative dielectric constant of the insulating material between the i-phase cable armor layer and the earth or seawater, r o_ia Indicates the outer radius of the armor layer of phase i cable, t ips_a Indicates the thickness of the insulation layer between the i-phase cable armor and the earth or seawater.

6. The method for calculating cable sequence parallel capacitance according to claim 1, wherein: The calculation expression for the parallel capacitance between the sheath layer of a single-core cable and the earth or seawater is as follows: Where: C isE Represents the parallel capacitance between the i-phase cable sheath and the earth or seawater, ε isE Represents the relative dielectric constant of the insulating material between the i-phase cable sheath and the earth or seawater, r o_is Indicates the outer radius of the i-phase cable sheath, t ips_s Indicates the thickness of the insulation layer between the i-phase cable sheath and the earth or seawater.

7. The method for calculating cable sequence parallel capacitance according to claim 1, wherein: For the parallel capacitance between the sheath layers of a three-core cable, the calculation expression is as follows: Where: C isjs Represents the parallel capacitance between the i-phase cable sheath layer and the j-phase cable sheath layer, ε 0sa Represents the relative dielectric constant of the insulating material between the sheath layer and the armor layer, r i_0a Indicates the inner radius of the armor layer, r o_is Indicates the outer radius of the i-phase cable sheath.

8. The method for calculating cable sequence parallel capacitance according to claim 1, wherein: For the parallel capacitance between the sheath and armor of a single-core cable, the calculation expression is as follows: Where: C isia Represents the parallel capacitance between the i-phase cable sheath and armor layer, ε isa Represents the relative dielectric constant of the insulating material between the i-phase cable sheath and armor layer, r i_ia Indicates the inner radius of the armor layer of phase i cable, r o_is Indicates the outer radius of the i-phase cable sheath.

9. The method for calculating cable sequence parallel capacitance according to claim 1, wherein: The calculation expression for the parallel capacitance between the sheath layer and the armor layer of a three-core cable is as follows: Where: C is0a Represents the parallel capacitance between the i-phase cable sheath and armor layer, ε 0sa Represents the relative dielectric constant of the insulating material between the sheath layer and the armor layer, r i_0a Indicates the inner radius of the armor layer, r o_is Represents the outer radius of the i-phase cable sheath, r o_ic Indicates the outer radius of the i-phase cable core layer.

10. The method for calculating cable sequence parallel capacitance according to claim 2 or 3, characterized in that: For single-core cables or three-core cables with fixed connections, the calculation expression of the phase parallel capacitance matrix is ​​as follows: C Phase =C cc For a single-core cable with an armored layer connected at a single point, the calculation expression for the parallel capacitance matrix is ​​as follows: For a single-core cable without armor layer using a single-point connection method, the calculation expression of its phase parallel capacitance matrix is ​​as follows: For a single-core cable with a cross-connection method, the calculation expression of its phase parallel capacitance matrix is ​​as follows: C Phase =C cc_new Where: C Phase Represents the phase parallel capacitance matrix, C cc_new is a diagonal capacitance matrix with equal diagonal elements, and its diagonal elements are C cc Mean of the diagonal elements.

11. The method for calculating cable sequence parallel capacitance according to claim 1, wherein: The calculation expression of the sequential parallel capacitance matrix is ​​as follows: Where: C ZPN Represents the sequence parallel capacitance matrix, the elements on the diagonal from top to bottom are zero sequence parallel capacitance, positive sequence parallel capacitance, negative sequence parallel capacitance, C Phase represents the phase parallel capacitance matrix, A is the phase sequence transformation matrix, a is a complex operator and a=e j120° , e is a natural constant, and j is an imaginary unit.

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