A method and system for calculating voltage along an offshore wind power sea cable based on distribution parameters

Abstract

This invention belongs to the field of power system operation and analysis technology, and discloses a method and system for calculating the voltage along a submarine cable for offshore wind power based on distributed parameters. It obtains grid-side parameters, wind farm-side parameters, and submarine cable line parameters, determines the series impedance per unit length, parallel admittance per unit length, propagation constant, and characteristic impedance of the submarine cable, and constructs an equivalent two-port admittance matrix. Using the output voltage phasor of the equivalent ideal current source of the wind farm as the reference phasor, and combining the terminal current boundary conditions and the grid-side voltage balance relationship, the voltage phasor at the beginning of the submarine cable and the phasor of the positive-sequence equivalent voltage source on the grid side are expressed as linear functions of the effective value of the output voltage. The unknown phase angle is eliminated using the positive-sequence voltage amplitude constraint on the grid side, the effective value of the output voltage is solved, and the effective voltage value at any position along the submarine cable is calculated using the distributed parameter transmission line equation. This invention can continuously calculate the voltage along the cable under wind farm load operation conditions, providing data support for submarine cable voltage stress assessment.

Description

Technical Field

[0001] This invention belongs to the field of power system operation and analysis technology, specifically relating to a method and system for calculating the voltage along a submarine cable for offshore wind power based on distributed parameters. Background Technology

[0002] As the distance from shore and the installed capacity of offshore wind farms continue to increase, the transmission distance of high-voltage AC submarine cables is also gradually increasing. Submarine cables have a large capacitance to ground per unit length, which generates significant charging current and reactive power under power frequency operation conditions. This causes the voltage along the cable to vary continuously, and under some operating conditions, the voltage in the middle of the cable or on the wind farm side may even exceed the rated voltage. Therefore, accurately obtaining the continuous voltage distribution along the submarine cable is a crucial foundation for conducting insulation configuration, voltage stress assessment, and operational safety analysis.

[0003] Chinese patent application CN109254189A discloses a method for calculating the terminal voltage of submarine cables during withstand voltage tests. This method derives the voltage calculation formula along the cable line using a distributed parameter model of the submarine cable and determines the core self-susceptance based on the equivalent capacitance model between different layers of the three-phase cable. The cable terminal voltage under withstand voltage test conditions is calculated by setting an equivalent capacitance at the cable end. This method is mainly applicable to cable withstand voltage test scenarios, and its boundary conditions are determined by the test power supply, terminal impedance, and equivalent capacitance. It does not address the solution of terminal voltage and current boundary quantities under the loaded grid-connected operation state of offshore wind farms.

[0004] Chinese patent application CN110046322A discloses an analytical calculation method for the core voltage of a long cable during withstand voltage testing. This method establishes Kirchhoff's equations based on the equivalent circuit considering the distributed parameters of the cable sheath. A single-phase cable transmission model is obtained through Laplace transform and inverse transform. The withstand voltage test boundary conditions, such as voltage applied to the core head, grounding of both ends of the sheath, and suspension of the core end, are substituted into the transmission model to calculate the cable core-to-ground voltage at different locations. While this method can consider the coupling relationship between the cable core and the sheath, its boundary conditions are also pre-set for the withstand voltage test conditions and cannot be directly used to solve for the boundary quantities at the cable end of a submarine cable that are jointly determined by the wind farm output state and the grid-side operating state during offshore wind farm operation under load and grid connection.

[0005] Chinese patent application CN116131276A discloses a method and system for optimizing reactive power compensation in offshore wind power based on power factor. It employs an equivalent circuit of distributed parameters of an AC submarine cable to calculate the voltage and current at any point along the cable based on the impedance per unit length, admittance per unit length, and known voltage and current at the cable's end. The capacity of the reactive power compensation device is then determined based on the reactive power deficit of the offshore wind farm. While this method reflects the distributed parameter characteristics of the AC submarine cable, its primary purpose is reactive power compensation capacity configuration. The voltage calculation along the cable requires known cable end voltage and current as boundary conditions. It does not provide a method for directly analytically solving for the boundary quantities at the cable end when the wind farm output current, wind farm equivalent internal impedance, grid-side equivalent internal impedance, and grid-side voltage phase angle are coupled together.

[0006] In summary, existing technologies can utilize distributed parameter transmission line models to calculate the voltage along a submarine cable or at a specific location given end boundary conditions. However, when offshore wind farms are connected to the grid under load, the voltage and current at the cable ends are simultaneously affected by the wind farm's output current, the wind farm's equivalent internal impedance, the grid's equivalent internal impedance, and the grid's voltage constraints. Therefore, not all end boundary quantities are known. If iterative power flow or electromagnetic transient simulations are first used to determine the end boundary quantities before calculating the voltage along the cable, the calculation process is relatively complex and time-consuming.

[0007] Therefore, there is an urgent need for a method that can directly solve the boundary quantities at the ends of submarine cables and continuously calculate the voltage at any position along the cable, taking into account the wind farm's operation under load and the distributed parameters of the submarine cable line. Summary of the Invention

[0008] The technical problem this invention aims to solve is that existing methods for calculating the voltage along submarine cables struggle to directly determine the end boundary quantities affected by the combined influence of the wind farm's output state, the grid's operating state, and the cable's distributed parameters under the condition of wind farms operating with loads and connected to the grid. This leads to the calculation of continuous voltage distribution along the cable relying on iterative power flow or electromagnetic transient simulations, resulting in complex and time-consuming calculations. To address this problem, this invention provides a method for calculating the voltage along a submarine wind power cable based on distributed parameters, comprising the following steps: S1, obtain the grid-side parameters, wind farm-side parameters and submarine cable parameters of the offshore wind power AC grid-connected system; S2, Based on the submarine cable line parameters, determine the series impedance per unit length, parallel admittance per unit length, propagation constant, and characteristic impedance of the submarine cable line, and construct the equivalent two-port admittance matrix of the submarine cable line. S3, construct an equivalent ideal current source for the wind farm based on the wind farm side parameters, and use the outlet voltage phasor of the equivalent ideal current source as a reference phasor to determine its effective voltage value. Let it be the variable to be determined; Based on the equivalent ideal current source of the wind farm, the positive sequence equivalent internal impedance of the wind farm, and the connection relationship between the ends of the submarine cable, the voltage phasor at the end of the submarine cable is expressed as a linear function of the variable to be determined. Based on the current boundary condition that the injected current phasor at the end of the submarine cable line is equal to the output current phasor of the equivalent ideal current source of the wind farm, and the equivalent two-port admittance matrix, the voltage phasor and the injected current phasor at the beginning of the submarine cable line are expressed as linear functions of the variables to be determined. Based on the voltage balance relationship on the power grid side, the voltage phasor at the beginning of the submarine cable line and the voltage drop phasor generated by the injected current phasor on the positive sequence equivalent internal impedance on the power grid side are added together to obtain the positive sequence equivalent voltage source phasor on the power grid side, and it is expressed as a linear function of the variable to be determined. S4. Based on the amplitude constraints of the positive-sequence equivalent voltage source phasors on the grid side, the corresponding linear function is squared to eliminate the unknown phase angle of the positive-sequence equivalent voltage source phasors on the grid side. An algebraic equation for the unknown variable is then constructed and solved to obtain the effective value of the outlet voltage of the equivalent ideal current source of the wind farm. ; S5, based on the effective value of the output voltage The voltage phasor and the injected current phasor at the beginning of the submarine cable line are calculated. Using the voltage phasor and the injected current phasor at the beginning of the submarine cable line as boundary conditions, the effective voltage value at any position along the submarine cable line is calculated through the distributed parameter transmission line equation, thus obtaining the voltage distribution along the submarine cable line.

[0009] Preferably, the grid-side parameters include the system reference voltage. System baseline capacity RMS value of phase voltage of the positive sequence equivalent voltage source on the grid side and the positive sequence equivalent internal impedance of the power grid side ; The wind farm-side parameters include the positive sequence output current of the wind farm. Axial components , Axial components and the positive sequence equivalent internal impedance of the wind farm Among them, the output voltage phasor direction of the equivalent ideal current source of the wind farm is taken as... In the positive direction of the axis, with the aforementioned Rotate counterclockwise in the positive direction of the axis direction as Positive direction of the axis; The submarine cable line parameters include the total length of the submarine cable line. And the per-unit value of the positive sequence series resistance of the entire submarine cable line. Positive sequence series reactance per unit value and positive sequence parallel current per unit value .

[0010] Preferably, the grid-side parameters include the system reference voltage. and system baseline capacity The submarine cable line parameters include the total length of the submarine cable line. And the per-unit value of the positive sequence series resistance of the entire submarine cable line. Positive sequence series reactance per unit value and positive sequence parallel current per unit value ; Wherein, the system reference voltage The system reference capacity is the line voltage reference value. This is the reference value for three-phase capacity; According to the system reference voltage and system baseline capacity Calculate the impedance reference value and admittance reference value :

[0011] Convert the per-unit parameters of the entire submarine cable line to series impedance per unit length. and unit length parallel admittance :

[0012] in, Represents the imaginary unit, and satisfies .

[0013] Preferably, the series impedance per unit length, the parallel admittance per unit length, and the total length of the submarine cable are respectively denoted as... , and The propagation constant and characteristic impedance They are respectively:

[0014] Wherein, the propagation constant Take the complex square root branch whose real part is not less than 0; when the propagation constant When the real part is equal to 0, the branch with an imaginary part not less than 0 is selected; the characteristic impedance Take the satisfaction Branches with a real part greater than 0; The equivalent two-port admittance matrix for:

[0015] in:

[0016] .

[0017] Preferably, the wind farm-side parameters include the positive sequence current output by the wind farm. Axial components , Axial components and the positive sequence equivalent internal impedance of the wind farm ; According to the above Axial components and Axial components Construct the output current phasor of the equivalent ideal current source of the wind farm:

[0018] in, Represents the imaginary unit, and satisfies ; The output voltage phasor of the equivalent ideal current source of the wind farm As a reference phasor, its phase angle is set to And its effective voltage value is recorded as ,but:

[0019] Voltage phasor at the end of the submarine cable line for:

[0020] The matrix elements of the equivalent two-port admittance matrix are respectively denoted as... , , and The voltage phasors and injected current phasors at the beginning and end of the submarine cable line satisfy the following:

[0021] The phasor of the current injected at the end of the submarine cable line satisfies: .

[0022] Preferably, the matrix elements of the equivalent two-port admittance matrix are respectively denoted as... , , and Let the positive-sequence equivalent internal impedance of the grid side, the positive-sequence equivalent internal impedance of the wind farm, and the output current phasor of the equivalent ideal current source of the wind farm be denoted as follows: , and ; The starting voltage phasor of the submarine cable line and the positive sequence equivalent voltage source phasor on the grid side They are represented as follows:

[0023] in:

[0024]

[0025]

[0026] .

[0027] Preferably, the linear functions of the head-end voltage phasor of the submarine cable line and the positive-sequence equivalent voltage source phasor on the grid side are expressed as follows:

[0028] The effective value of the phase voltage of the positive-sequence equivalent voltage source on the grid side is denoted as... According to the amplitude constraints of the positive-sequence equivalent voltage source phasors on the grid side:

[0029] Building about Algebraic equations:

[0030] in:

[0031]

[0032]

[0033] To take the real part of a complex number, This indicates taking the imaginary part of a complex number; The real roots of the algebraic equation that are greater than zero and satisfy the operating voltage constraints of the offshore wind power AC grid-connected system are selected as the effective value of the output voltage. When there are multiple real roots that meet the conditions, select the real root with the smallest difference from the system's rated phase voltage. The system rated phase voltage Based on the system's rated line voltage Determined according to the following formula:

[0034] The system's rated line voltage This is the nominal line voltage of the offshore wind power AC grid-connected system, obtained based on system design parameters or equipment rated parameters; The operating voltage constraint is:

[0035] in, and These are the lower and upper limits of the voltage corresponding to the allowable voltage deviation range, respectively. The allowable voltage deviation range is determined based on the grid connection technology requirements, voltage quality standards, or engineering design requirements applicable to the offshore wind power AC grid-connected system, and is used as a preset parameter. According to the effective value of the output voltage calculate:

[0036]

[0037]

[0038] Let the propagation constant, characteristic impedance, and total length of the submarine cable be denoted as... , and The distance along the submarine cable line from the end of the submarine cable on the power grid side The effective voltage value at that point is: .

[0039] A system for calculating the voltage along a submarine cable for offshore wind power based on distributed parameters, comprising: The parameter acquisition module is used to acquire grid-side parameters, wind farm-side parameters, and submarine cable line parameters of the offshore wind power AC grid-connected system. The distributed parameter model construction module is used to determine the series impedance per unit length, parallel admittance per unit length, propagation constant, and characteristic impedance of the submarine cable line based on the submarine cable line parameters, and to construct the equivalent two-port admittance matrix of the submarine cable line. The boundary relationship construction module is used to construct an equivalent ideal current source for the wind farm based on the wind farm side parameters, using the outlet voltage phasor of the equivalent ideal current source as a reference phasor, and setting its effective voltage value. Let these be the variables to be determined, and in conjunction with the current boundary conditions at the end of the submarine cable line, the equivalent two-port admittance matrix, and the voltage balance relationship on the grid side, express the head-end voltage phasor and the positive-sequence equivalent voltage source phasor on the grid side as the effective value of the output voltage. A linear function; The voltage calculation module is used to substitute the linear function of the positive-sequence equivalent voltage source phasor on the grid side into its amplitude constraint, and take the square of the modulus of the linear function to eliminate the unknown phase angle of the positive-sequence equivalent voltage source phasor on the grid side, thereby constructing and solving for the effective value of the output voltage. Algebraic equations; The line voltage calculation module is used to calculate the effective value of the output voltage. Calculate the voltage phasor and injected current phasor at the beginning of the submarine cable line, and calculate the effective voltage value at any location along the submarine cable line using the distributed parameter transmission line equation.

[0040] Compared with the prior art, the beneficial effects of the present invention are: This invention uses distributed transmission line parameters to describe the series impedance and parallel admittance of submarine cables, preserving the characteristic of continuous parameter distribution along the long-distance submarine cable line. By equating the wind farm with a combination of an ideal current source and equivalent internal impedance, and combining the equivalent two-port admittance matrix of the submarine cable with the amplitude constraints of the positive-sequence equivalent voltage source phasor on the grid side, the solution of the boundary quantities at the end of the submarine cable is transformed into an algebraic equation concerning the effective value of the outlet voltage of the equivalent ideal current source of the wind farm, reducing the dependence on iterative power flow or electromagnetic transient simulation. After obtaining the voltage phasor and the injected current phasor at the beginning of the submarine cable, the effective voltage value at any position along the submarine cable is continuously calculated using the distributed parameter transmission line equation, thereby reducing the calculation time of voltage analysis along long-distance submarine cables under load and providing data support for submarine cable voltage stress assessment and operational safety analysis. Attached Figure Description

[0041] Figure 1 This is a flowchart of the method for calculating the voltage along the submarine cable of offshore wind power based on distributed parameters according to the present invention.

[0042] Figure 2 This is the positive sequence equivalent circuit diagram of the offshore wind power AC grid-connected system of the present invention.

[0043] Figure 3 This is a graph showing the distribution curve of the effective value of the positive sequence phase voltage along the submarine cable in an embodiment of the present invention. Detailed Implementation

[0044] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments. It should be understood that the described embodiments are only for illustrating the present invention and are not intended to limit the scope of protection of the present invention.

[0045] In this invention, voltage and current phasors are characterized by their effective values. Symbols with dots represent phasors, and those without dots represent effective values. The submarine cable is a uniformly distributed AC submarine cable, and insulation leakage conductance is ignored. The beginning of the submarine cable is the end closest to the power grid, and the end is the end closest to the wind farm; position variables... Indicates the distance between the corresponding location and the end of the submarine cable on the power grid side; the phasor of the current injected at the beginning of the submarine cable line. and the phasor of the injected current at the end The positive direction of all points is towards the interior of the submarine cable line.

[0046] like Figure 1 and Figure 2 As shown in the figure, this embodiment provides a method for calculating the voltage along a submarine cable for offshore wind power based on distributed parameters, which specifically includes the following steps.

[0047] S1: Obtain grid-side parameters, wind farm-side parameters, and submarine cable line parameters of the offshore wind power AC grid-connected system.

[0048] Grid-side parameters include system reference voltage. System baseline capacity RMS value of phase voltage of the positive sequence equivalent voltage source on the grid side and the positive sequence equivalent internal impedance of the power grid side Among them, the system reference voltage The line voltage reference value and the system reference capacity are given. This is the reference value for three-phase capacity.

[0049] Wind farm-side parameters include the positive sequence output current of the wind farm. Axial components , Axial components and the positive sequence equivalent internal impedance of the wind farm The output voltage phasor direction of the equivalent ideal current source of the wind farm is taken as... In the positive direction of the axis, with the aforementioned Rotate counterclockwise in the positive direction of the axis direction as Positive axis direction and These represent the positive sequence current phasors output by the wind farm at... shaft and The components on the axis are all characterized according to the effective value of the phase current.

[0050] Submarine cable parameters include the total length of the submarine cable. And the per-unit value of the positive sequence series resistance of the entire submarine cable line. Positive sequence series reactance per unit value and positive sequence parallel current per unit value .

[0051] in, "Always" represents the per-unit value of the positive-sequence series reactance of the entire submarine cable line, and the location variable. "Always" indicates the distance between the corresponding location and the end of the submarine cable on the power grid side; the two have different meanings.

[0052] To select the effective value of the output voltage that meets the actual operating requirements, the system's rated line voltage was also obtained. and the allowable voltage deviation range. System rated line voltage. The nominal line voltage of the offshore wind power AC grid-connected system can be obtained based on the system design parameters or equipment rated parameters; the allowable voltage deviation range is determined according to the grid connection technical requirements, voltage quality standards or engineering design requirements applicable to the offshore wind power AC grid-connected system.

[0053] S2: Construct the equivalent two-port admittance matrix of the submarine cable line, as follows: Based on the system reference voltage and system baseline capacity Calculate the impedance reference value and admittance reference value :

[0054]

[0055] Convert the per-unit parameters of the entire submarine cable line to series impedance per unit length. and unit length parallel admittance :

[0056]

[0057] in, The unit is , The unit is ; Represents the imaginary unit, and satisfies .

[0058] Based on the series impedance per unit length and unit length parallel admittance Calculate the complex propagation constant of the submarine cable line. and complex characteristic impedance :

[0059]

[0060] Among them, the propagation constant Take the real part not less than The complex square root branch; when the propagation constant The real part equals When, the imaginary part is not less than The branch. In determining the propagation constant. After that, characteristic impedance Take the satisfaction And the real part is greater than The branches are designed to ensure that the values ​​of the propagation constant and characteristic impedance remain consistent.

[0061] Based on the distributed parameter transmission line equation, the equivalent two-port admittance matrix of the submarine cable line is constructed:

[0062] in:

[0063]

[0064] and For self-guided admittance, and For mutual admittance.

[0065] S3: Construct the end boundary relationships, as follows: Based on the positive sequence current output of the wind farm Axial components and Axial components Construct the output current phasor of the equivalent ideal current source of the wind farm:

[0066] The output voltage phasor of the equivalent ideal current source of the wind farm As a reference phasor, its phase angle is set to And its effective voltage value is recorded as ,but:

[0067] in:

[0068] Based on the equivalent ideal current source of the wind farm, the positive-sequence equivalent internal impedance of the wind farm, and the connection relationship between the ends of the submarine cable, the voltage phasor at the end of the submarine cable is... for:

[0069] Therefore, the voltage phasor at the end of the submarine cable line Represented as the variable to be solved A linear function.

[0070] The voltage phasor and injected current phasor at the beginning and end of the submarine cable line satisfy the following:

[0071] Since the wind farm, as an equivalent ideal current source, injects current into the end of the submarine cable, the phasor of the current injected into the end of the submarine cable satisfies:

[0072] Will:

[0073] as well as:

[0074] Substituting the second row of the equivalent two-port admittance matrix:

[0075] get:

[0076] in:

[0077]

[0078] According to the first row of the equivalent two-port admittance matrix, we can obtain:

[0079] because and All are variables to be determined The linear function, therefore, the current phasor injected at the beginning of the submarine cable line. It can also be represented as the variable to be determined. A linear function.

[0080] Based on the positive-sequence equivalent voltage source on the power grid side, the positive-sequence equivalent internal impedance on the power grid side, and the connection relationship between the beginning and end of the submarine cable line, the voltage phasor at the beginning of the submarine cable line... Phasor of the first-end injected current Positive sequence equivalent internal impedance on the grid side The voltage drop phasors generated above are added together to obtain the positive-sequence equivalent voltage source phasors on the grid side:

[0081] The first row of the equivalent two-port admittance matrix, the voltage phasor at the end of the submarine cable line, and:

[0082] Substituting the voltage balance relationship into the grid side, we get:

[0083] in:

[0084]

[0085] Therefore, the voltage phasor at the end of the submarine cable line, the voltage phasor at the beginning of the cable line, the current injected at the beginning of the cable line, and the positive-sequence equivalent voltage source phasor on the power grid side are all represented as variables to be determined. A linear function.

[0086] S4: Solve for the effective value of the output voltage, as follows: Positive sequence equivalent voltage source phasor on the grid side The phase angle is unknown, but the effective value of its phase voltage is unknown. Given that, therefore, the following conditions are met:

[0087] Will:

[0088] Substituting the above amplitude constraints and taking the square of the modulus of the linear function, the positive-sequence equivalent voltage source phasors on the grid side are eliminated. The unknown phase angle, to obtain information about Algebraic equations:

[0089] in:

[0090]

[0091]

[0092] In the formula, To take the real part of a complex number, This indicates taking the imaginary part of a complex number.

[0093] Solve the above algebraic equation, and select real roots that are greater than zero and satisfy the operating voltage constraints of the offshore wind power AC grid-connected system from all its real roots. These selected real roots are then used as candidate real roots. If multiple candidate real roots exist, the one with the smallest difference from the system's rated phase voltage is selected and used as the effective value of the output voltage of the equivalent ideal current source of the wind farm. .

[0094] System rated phase voltage Based on the system's rated line voltage Determined according to the following formula:

[0095] System rated line voltage This is the nominal line voltage of the offshore wind power AC grid-connected system, obtained based on system design parameters or equipment rated parameters.

[0096] The operating voltage constraint is:

[0097] in, and These are the lower and upper limits of the allowable voltage deviation range, respectively. The allowable voltage deviation range is determined based on the grid connection technology requirements, voltage quality standards, or engineering design requirements applicable to the offshore wind power AC grid-connected system, and is used as a preset parameter.

[0098] S5: Calculate the voltage along the submarine cable, as follows: Based on the obtained effective value of the output voltage Calculate the voltage phasor at the beginning of the submarine cable line, the voltage phasor at the end of the submarine cable line, and the phasor of the current injected at the beginning of the submarine cable line:

[0099]

[0100]

[0101] Using the voltage phasor at the beginning of the submarine cable line and the phasor of the injected current at the beginning As a boundary condition, the distance from the end of the submarine cable on the power grid side is calculated using the distributed parameter transmission line equation. Voltage phasor at:

[0102] By taking the modulus of the voltage phasor, the distance from the end of the submarine cable on the power grid side is obtained. RMS voltage at:

[0103] Through the interval Multiple calculation locations are set up internally, and the effective voltage value of each calculation location is calculated. The calculation locations are arranged in order of distance between each calculation location and the end of the submarine cable on the power grid side, so that the voltage distribution along the submarine cable line can be obtained, providing a calculation basis for voltage stress assessment along the submarine cable line.

[0104] For ease of understanding, such as Figure 3As shown, this embodiment is used to illustrate the specific calculation process and verification results of the above method.

[0105] In this embodiment, the system reference voltage for System baseline capacity for The effective value of the phase voltage of the positive sequence equivalent voltage source on the grid side. for The corresponding effective value of the line voltage is Positive sequence equivalent internal impedance of the power grid side for:

[0106] The positive sequence current output of the wind farm Axial components for , Axial components for Positive-sequence equivalent internal impedance of a wind farm for:

[0107] The total length of the submarine cable line for The per-unit value of the positive sequence series resistance of the entire submarine cable line. for Positive sequence series reactance per unit value for The per-unit value of the parallel-connected current in the positive sequence for .

[0108] Based on the parameters above, the following can be calculated:

[0109]

[0110] Converting the per-unit parameters of the entire submarine cable line to named parameters per unit length yields:

[0111]

[0112] Further calculations yielded the following:

[0113]

[0114] The self-admittance and mutual admittance in the equivalent two-port admittance matrix are as follows:

[0115]

[0116] The output current phasor of the equivalent ideal current source of a wind farm is:

[0117] The calculation yielded:

[0118]

[0119]

[0120]

[0121] From this, we can obtain information about The quadratic equation of :

[0122] The two real roots of the equation are approximately... and .

[0123] In this embodiment, the system rated line voltage for The rated phase voltage of the system is calculated based on the rated line voltage of the system:

[0124] To illustrate the process of selecting candidate real roots, this embodiment sets the operating voltage constraint as follows:

[0125] Accordingly:

[0126] in, The physical condition that the effective value of the voltage is greater than zero is not met, nor is the operating voltage constraint. It is greater than zero and within the operating voltage constraint range, therefore it is determined that:

[0127] Further calculations yielded the voltage phasor at the beginning of the submarine cable line:

[0128] Voltage phasor at the end of the submarine cable line:

[0129] Current phasor injected at the beginning of the submarine cable line:

[0130] Will and Substituting into the distributed parameter transmission line equation, the effective value distribution of the positive sequence phase voltage along the submarine cable line is obtained. The distance from the end of the submarine cable on the power grid side is selected. , and The position was calculated, and the results are shown in Table 1 below: Table 1 Test Data

[0131] The absolute relative error is calculated using the following formula:

[0132] In the formula, This represents the calculated value using this method. This represents the simulated measurement value.

[0133] The results in the table show that the maximum absolute relative error of this method at the three verification locations is: This indicates that the analytical calculation results are in good agreement with the PSCAD / EMTDC steady-state simulation results.

[0134] Under the same computer configuration, input parameters, and operating conditions, the PSCAD / EMTDC model takes approximately 1 minute and 57 seconds to go from startup to steady state. The time taken by this method to complete one calculation of end boundary quantities and voltage distribution along the line is approximately... Seconds. Therefore, this method can reduce the calculation time for voltage analysis along the offshore wind power AC transmission cable while maintaining the accuracy of voltage calculation along the cable.

[0135] This embodiment also provides a system for calculating the voltage along a submarine wind power cable based on distributed parameters, used to execute the aforementioned method for calculating the voltage along a submarine wind power cable based on distributed parameters. The system includes a parameter acquisition module, a distributed parameter model construction module, a boundary relationship construction module, a voltage solution module, and a voltage calculation module along the cable.

[0136] The parameter acquisition module is used to acquire grid-side parameters, wind farm-side parameters, and submarine cable line parameters of the offshore wind power AC grid-connected system.

[0137] Among them, the grid-side parameters include the system reference voltage. System baseline capacity RMS value of phase voltage of the positive sequence equivalent voltage source on the grid side and the positive sequence equivalent internal impedance of the power grid side Wind farm-side parameters include the positive sequence output current of the wind farm. Axial components , Axial components and the positive sequence equivalent internal impedance of the wind farm Submarine cable line parameters include the total length of the submarine cable line. And the per-unit value of the positive sequence series resistance of the entire submarine cable line. Positive sequence series reactance per unit value and positive sequence parallel current per unit value .

[0138] The parameter acquisition module can also acquire the system's rated line voltage. and the allowable voltage deviation range. System rated line voltage. The allowable voltage deviation range can be obtained from the system design parameters or equipment rated parameters, and can be determined from the grid connection technical requirements, voltage quality standards or engineering design requirements applicable to the offshore wind power AC grid-connected system.

[0139] The distributed parameter model building module is used to determine the series impedance per unit length of a submarine cable line based on the cable line parameters. and unit length parallel admittance Based on the series impedance per unit length and unit length parallel admittance Calculate the propagation constant and characteristic impedance Based on the distributed parameter transmission line equation, the equivalent two-port admittance matrix of the submarine cable line is constructed. .

[0140] Specifically, the distributed parameter model construction module first uses the system reference voltage... and system baseline capacity Calculate the impedance reference value and admittance reference value Then, the per-unit parameters of the entire submarine cable line are converted into named parameters per unit length. The calculation methods for the propagation constant, characteristic impedance, and equivalent two-port admittance matrix are the same as those described above, and will not be repeated here.

[0141] The boundary relationship construction module is used to determine the positive sequence current output by the wind farm. Axial components and Axial components Construct the output current phasor of the equivalent ideal current source of the wind farm:

[0142] The boundary relation construction module is also used to construct the output voltage phasor of the wind farm equivalent ideal current source. As a reference phasor, its phase angle is set to and its effective voltage value Set as the variable to be determined; based on the equivalent ideal current source of the wind farm and the positive sequence equivalent internal impedance of the wind farm. The connection relationship between the submarine cable line and its end is used to determine the voltage phasor at the end of the submarine cable line:

[0143] The boundary relationship construction module further considers the boundary conditions satisfied by the injected current phasor at the end of the submarine cable line:

[0144] And the equivalent two-port admittance matrix of the submarine cable line, expressing the head-end voltage phasor and head-end injected current phasor as the effective value of the output voltage. A linear function.

[0145] The boundary relationship construction module is also used to determine the positive-sequence equivalent internal impedance of the submarine cable's head-end voltage phasor and head-end injected current phasor on the grid side based on the grid-side voltage balance relationship. The voltage drop phasors generated on the cable are added together to obtain the positive-sequence equivalent voltage source phasor on the grid side. The voltage phasor at the beginning of the submarine cable line and the positive-sequence equivalent voltage source phasor on the grid side are expressed as follows:

[0146]

[0147] in, , , and The calculation method is the same as the method described above.

[0148] The voltage solver module is used to determine the magnitude constraints of the positive-sequence equivalent voltage source phasors on the grid side.

[0149] The linear function of the positive-sequence equivalent voltage source phasor on the grid side:

[0150] Substituting the amplitude constraint and taking the square of the modulus of the linear function to eliminate the unknown phase angle of the positive-sequence equivalent voltage source phasors on the grid side, a method for constructing the effective value of the output voltage is developed. Algebraic equations:

[0151] The voltage solving module solves the algebraic equation and selects real roots that are greater than zero and satisfy the operating voltage constraints of the offshore wind power AC grid-connected system from the real roots. If multiple real roots satisfy the conditions, the real root with the smallest difference from the rated phase voltage of the system is selected as the effective value of the output voltage of the equivalent ideal current source of the wind farm. .

[0152] The system's rated phase voltage is calculated based on the system's rated line voltage. The lower and upper limits of the operating voltage constraints are determined according to the grid connection technical requirements, voltage quality standards, or engineering design requirements applicable to the offshore wind power AC grid-connected system.

[0153] The line voltage calculation module is used to calculate the effective value of the output voltage. Calculate the voltage phasor at the beginning of the submarine cable line, the voltage phasor at the end of the submarine cable line, and the phasor of the current injected at the beginning of the submarine cable line:

[0154]

[0155]

[0156] The voltage calculation module along the line further uses and As a boundary condition, the distance from the end of the submarine cable on the power grid side is calculated. RMS voltage at:

[0157] The voltage calculation module along the line can calculate the voltage in the interval according to a preset distance. Multiple calculation locations are set up internally, and the effective voltage value of each calculation location is calculated. The voltage distribution data or voltage distribution curve along the submarine cable is generated in sequence according to the distance between each calculation location and the end of the submarine cable on the power grid side.

[0158] It should be noted that the parameter acquisition module, distributed parameter model construction module, boundary relationship construction module, voltage solution module, and line voltage calculation module are logical modules divided according to their data processing functions. These modules can be implemented by software programs or by a processor, memory, and corresponding hardware circuits. Without changing the data processing procedure, multiple modules can be combined, and a single module can be divided into multiple sub-modules based on its execution function.

[0159] This embodiment also provides an electronic device, which includes a processor and a memory. The memory stores a computer program. When the computer program is executed by the processor, it causes the processor to perform the above-described method for calculating the voltage along the offshore wind power cable based on distributed parameters.

[0160] The processor can be a central processing unit, a digital signal processor, a microprocessor, or other processing device with data processing capabilities. The memory can include random access memory, read-only memory, non-volatile memory, or a combination of the above. The processor and memory can be connected via a communication bus.

[0161] This embodiment also provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the above-described method for calculating the voltage along the submarine cable of offshore wind power based on distributed parameters.

[0162] The computer-readable storage medium may be a read-only memory, random access memory, disk, optical disk, flash memory, portable hard drive, or other medium capable of storing and being read by a processor from a computer program.

Claims

1. A method for calculating the voltage along a submarine cable for offshore wind power based on distributed parameters, characterized in that, include: S1, obtain the grid-side parameters, wind farm-side parameters and submarine cable parameters of the offshore wind power AC grid-connected system; S2, Based on the submarine cable line parameters, determine the series impedance per unit length, parallel admittance per unit length, propagation constant, and characteristic impedance of the submarine cable line, and construct the equivalent two-port admittance matrix of the submarine cable line. S3, construct an equivalent ideal current source for the wind farm based on the wind farm side parameters, and use the outlet voltage phasor of the equivalent ideal current source as a reference phasor to determine its effective voltage value. Let it be the variable to be determined; Based on the equivalent ideal current source of the wind farm, the positive sequence equivalent internal impedance of the wind farm, and the connection relationship between the ends of the submarine cable, the voltage phasor at the end of the submarine cable is expressed as a linear function of the variable to be determined. Based on the current boundary condition that the injected current phasor at the end of the submarine cable line is equal to the output current phasor of the equivalent ideal current source of the wind farm, and the equivalent two-port admittance matrix, the voltage phasor and the injected current phasor at the beginning of the submarine cable line are expressed as linear functions of the variables to be determined. Based on the voltage balance relationship on the power grid side, the voltage phasor at the beginning of the submarine cable line and the voltage drop phasor generated by the injected current phasor on the positive sequence equivalent internal impedance on the power grid side are added together to obtain the positive sequence equivalent voltage source phasor on the power grid side, and it is expressed as a linear function of the variable to be determined. S4. Based on the amplitude constraints of the positive-sequence equivalent voltage source phasors on the grid side, the corresponding linear function is squared to eliminate the unknown phase angle of the positive-sequence equivalent voltage source phasors on the grid side. An algebraic equation for the unknown variable is then constructed and solved to obtain the effective value of the outlet voltage of the equivalent ideal current source of the wind farm. ; S5, based on the effective value of the output voltage The voltage phasor and the injected current phasor at the beginning of the submarine cable line are calculated. Using the voltage phasor and the injected current phasor at the beginning of the submarine cable line as boundary conditions, the effective voltage value at any position along the submarine cable line is calculated through the distributed parameter transmission line equation, thus obtaining the voltage distribution along the submarine cable line.

2. The method for calculating the voltage along a submarine wind power cable based on distributed parameters according to claim 1, characterized in that, The grid-side parameters include the system reference voltage. System baseline capacity RMS value of phase voltage of the positive sequence equivalent voltage source on the grid side and the positive sequence equivalent internal impedance of the power grid side ; The wind farm-side parameters include the positive sequence output current of the wind farm. Axial components , Axial components and the positive sequence equivalent internal impedance of the wind farm Among them, the output voltage phasor direction of the equivalent ideal current source of the wind farm is taken as... In the positive direction of the axis, with the aforementioned Rotate counterclockwise in the positive direction of the axis direction as Positive direction of the axis; The submarine cable line parameters include the total length of the submarine cable line. And the per-unit value of the positive sequence series resistance of the entire submarine cable line. Positive sequence series reactance per unit value and positive sequence parallel current per unit value .

3. The method for calculating the voltage along a submarine wind power cable based on distributed parameters according to claim 1, characterized in that, The grid-side parameters include the system reference voltage. and system baseline capacity The submarine cable line parameters include the total length of the submarine cable line. And the per-unit value of the positive sequence series resistance of the entire submarine cable line. Positive sequence series reactance per unit value and positive sequence parallel current per unit value ; Wherein, the system reference voltage The system reference capacity is the line voltage reference value. This is the reference value for three-phase capacity; According to the system reference voltage and system baseline capacity Calculate the impedance reference value and admittance reference value : Convert the per-unit parameters of the entire submarine cable line to series impedance per unit length. and unit length parallel admittance : in, Represents the imaginary unit, and satisfies .

4. The method for calculating the voltage along a submarine wind power cable based on distributed parameters according to claim 1, characterized in that, Let the unit length series impedance, unit length parallel admittance, and total length of the submarine cable be denoted as... , and The propagation constant and characteristic impedance They are respectively: Wherein, the propagation constant Take the complex square root branch whose real part is not less than 0; when the propagation constant When the real part is equal to 0, the branch with an imaginary part not less than 0 is selected; the characteristic impedance Take the satisfaction Branches with a real part greater than 0; The equivalent two-port admittance matrix for: in: 。 5. The method for calculating the voltage along a submarine wind power cable based on distributed parameters according to claim 2, characterized in that, The wind farm-side parameters include the positive sequence output current of the wind farm. Axial components , Axial components and the positive sequence equivalent internal impedance of the wind farm ; According to the above Axial components and Axial components Construct the output current phasor of the equivalent ideal current source of the wind farm: in, Represents the imaginary unit, and satisfies ; The output voltage phasor of the equivalent ideal current source of the wind farm As a reference phasor, its phase angle is set to And its effective voltage value is recorded as ,but: Voltage phasor at the end of the submarine cable line for: The matrix elements of the equivalent two-port admittance matrix are respectively denoted as... , , and The voltage phasors and injected current phasors at the beginning and end of the submarine cable line satisfy the following: The phasor of the current injected at the end of the submarine cable line satisfies: 。 6. The method for calculating the voltage along a submarine wind power cable based on distributed parameters according to claim 5, characterized in that, The matrix elements of the equivalent two-port admittance matrix are respectively denoted as... , , and Let the positive-sequence equivalent internal impedance of the grid side, the positive-sequence equivalent internal impedance of the wind farm, and the output current phasor of the equivalent ideal current source of the wind farm be denoted as follows: , and ; The starting voltage phasor of the submarine cable line and the positive sequence equivalent voltage source phasor on the grid side They are represented as follows: in: 。 7. The method for calculating the voltage along a submarine wind power cable based on distributed parameters according to claim 6, characterized in that, The linear functions of the head-end voltage phasor and the positive-sequence equivalent voltage source phasor on the grid side of the submarine cable line are expressed as follows: The effective value of the phase voltage of the positive-sequence equivalent voltage source on the grid side is denoted as... According to the amplitude constraints of the positive-sequence equivalent voltage source phasors on the grid side: Building about Algebraic equations: in: To take the real part of a complex number, This indicates taking the imaginary part of a complex number; The real roots of the algebraic equation that are greater than zero and satisfy the operating voltage constraints of the offshore wind power AC grid-connected system are selected as the effective value of the output voltage. When there are multiple real roots that meet the conditions, select the real root with the smallest difference from the system's rated phase voltage. The system rated phase voltage Based on the system's rated line voltage Determined according to the following formula: The system's rated line voltage This is the nominal line voltage of the offshore wind power AC grid-connected system, obtained based on system design parameters or equipment rated parameters; The operating voltage constraint is: in, and These are the lower and upper limits of the voltage corresponding to the allowable voltage deviation range, respectively. The allowable voltage deviation range is determined based on the grid connection technology requirements, voltage quality standards, or engineering design requirements applicable to the offshore wind power AC grid-connected system, and is used as a preset parameter. According to the effective value of the output voltage calculate: Let the propagation constant, characteristic impedance, and total length of the submarine cable be denoted as... , and The distance along the submarine cable line from the end of the submarine cable on the power grid side The effective voltage value at that point is: 。 8. A system for calculating the voltage along a submarine wind power cable based on distributed parameters, used to execute the method for calculating the voltage along a submarine wind power cable based on distributed parameters according to any one of claims 1 to 7, characterized in that, include: The parameter acquisition module is used to acquire grid-side parameters, wind farm-side parameters, and submarine cable line parameters of the offshore wind power AC grid-connected system. The distributed parameter model construction module is used to determine the series impedance per unit length, parallel admittance per unit length, propagation constant, and characteristic impedance of the submarine cable line based on the submarine cable line parameters, and to construct the equivalent two-port admittance matrix of the submarine cable line. The boundary relationship construction module is used to construct an equivalent ideal current source for the wind farm based on the wind farm side parameters, using the outlet voltage phasor of the equivalent ideal current source as a reference phasor, and setting its effective voltage value. Let these be the variables to be determined, and in conjunction with the current boundary conditions at the end of the submarine cable line, the equivalent two-port admittance matrix, and the voltage balance relationship on the grid side, express the head-end voltage phasor and the positive-sequence equivalent voltage source phasor on the grid side as the effective value of the output voltage. A linear function; The voltage calculation module is used to substitute the linear function of the positive-sequence equivalent voltage source phasor on the grid side into its amplitude constraint, and take the square of the modulus of the linear function to eliminate the unknown phase angle of the positive-sequence equivalent voltage source phasor on the grid side, thereby constructing and solving for the effective value of the output voltage. Algebraic equations; The line voltage calculation module is used to calculate the effective value of the output voltage. Calculate the voltage phasor and injected current phasor at the beginning of the submarine cable line, and calculate the effective voltage value at any location along the submarine cable line using the distributed parameter transmission line equation.

9. An electronic device, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the method for calculating the voltage along the offshore wind power submarine cable based on distributed parameters, as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for calculating the voltage along the offshore wind power submarine cable based on distributed parameters, as described in any one of claims 1 to 7.

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