Offshore wind power flexible low-frequency output capacity analysis method and system

Abstract

The invention provides an offshore wind power flexible low-frequency output capacity analysis method and system, and the method comprises the steps: building a mathematical model which comprises low-frequency bus AC voltage, low-frequency bus reactive power, power-frequency bus AC voltage, on-load voltage regulation tap switch gears and equipment parameters; operation constraints of modulation degree, transformer capacity, valve side voltage, valve side current and bridge arm current are introduced; calculating a plurality of sub power circles for different boundary combinations and tap switch gears based on the mathematical model; and obtaining an intersection of the sub-power circles under the same gear to obtain a power operation range of the gear, and obtaining a union set of the power operation ranges of different gears to obtain a complete power operation range of the flexible low-frequency power transmission system. According to the method, a clear technical basis is provided for equipment type selection, parameter optimization and scheme comparison and selection of the flexible low-frequency power transmission system, the project investment cost is reduced, and the submarine cable transmission capacity is improved.

Description

Technical Field

[0001] This invention relates to the field of flexible low-frequency power transmission technology, and in particular to a method and system for analyzing the flexible low-frequency power transmission capacity of offshore wind power. Background Technology

[0002] As nearshore resources become increasingly scarce, wind power is expanding into offshore areas. However, long-distance power frequency AC transmission suffers from significant reactive power losses and limited cable current carrying capacity. Flexible DC transmission is suitable for large-scale long-distance transmission, but the cost of rebuilding offshore converter stations is high. Therefore, flexible low-frequency AC transmission is a beneficial supplement to power frequency AC transmission and flexible DC transmission. Flexible low-frequency AC transmission offers technical and economic advantages such as improved line transmission capacity and reduced engineering investment costs, and can be applied to medium- and long-distance offshore wind power transmission. The Modular Multilevel Matrix Converter (M3C), based on a full-bridge structure, offers advantages such as modularity, controllable power factors on both the power frequency and low-frequency sides, fast dynamic response, and flexible power flow control. It can achieve AC-AC conversion and is used for flexible low-frequency AC transmission.

[0003] Currently, research on flexible low-frequency power transmission is still focused on basic theory, control strategies, simulation verification, and experimental prototypes, with a small number of demonstration projects already in operation.

[0004] The analysis of flexible low-frequency transmission capacity for offshore wind power is fundamental for system parameter selection, scheme comparison, and determination of applicable scope; therefore, accurate analysis and calculation are necessary. Frequency variations, reactive power compensation, and changes in laying conditions for different sections of submarine cables can all cause variations in the current-carrying capacity of the submarine cables. To accurately analyze the flexible low-frequency transmission capacity and improve the parameter design and economic efficiency of flexible low-frequency transmission systems, there is an urgent need to design a method and system for analyzing the flexible low-frequency transmission capacity of offshore wind power. Summary of the Invention

[0005] The main objective of this invention is to provide a method and system for analyzing the transmission capacity of flexible low-frequency offshore wind power, which solves the problem in the prior art of lacking a method and system for accurately and efficiently analyzing the transmission capacity of flexible low-frequency offshore wind power systems under conditions of multivariate coupling and parameter uncertainty.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for analyzing the flexible low-frequency transmission capacity of offshore wind power, the method comprising: A mathematical model is established that includes low-frequency bus AC voltage, low-frequency bus reactive power, power frequency bus AC voltage, on-load tap changer position and equipment parameters, and operational constraints such as modulation index, transformer capacity, valve side voltage, valve side current and bridge arm current are introduced. Based on the mathematical model, multiple sub-power circles are calculated for different boundary combinations and tap changer positions. The power operating range of a given range is obtained by taking the intersection of the sub-power circles under the same range and then taking the union of the power operating ranges of different ranges.

[0007] In the preferred scheme, the regulation constraint is that the regulation m satisfies ,in and Determined by the characteristics of the converter valve.

[0008] In the preferred embodiment, the transformer capacity constraint includes: Calculate the lower boundary value of reactive power based on the assumption that the apparent power on the grid side does not exceed the rated capacity of the transformer. ; Calculate the upper boundary value of reactive power based on the assumption that the apparent power on the valve side does not exceed the rated capacity of the transformer. ; comprehensive and Determine the reactive power boundary q.

[0009] In the preferred embodiment, the power is viewed from the grid side. With rated capacity satisfy and active power With reactive power satisfy ; Valve side view in power With rated capacity satisfy and active power With reactive power satisfy .

[0010] In the preferred embodiment, the valve-side voltage constraint is that the power frequency valve-side voltage does not exceed the maximum allowable value. , Valve-side current constraint: The power frequency valve-side current does not exceed the maximum allowable value. .

[0011] In the preferred embodiment, the arm current constraint is that the arm current does not exceed the maximum allowable value. .

[0012] In the preferred scheme, the calculation of the sub-power circle includes: Multiple values ​​of the low-frequency bus AC voltage are selected within its minimum, maximum, and intermediate ranges. These values ​​are then combined with the boundary values ​​of the low-frequency bus reactive power, the boundary values ​​of the power frequency bus AC voltage, and different on-load tap changer positions and input into the mathematical model.

[0013] In the preferred embodiment, the steps for establishing a mathematical model that includes equipment parameters include: Constructing a multivariable coupled sensitivity matrix ; Wherein, the state vector , This indicates the low-frequency bus AC voltage. Indicates the reactive power of the low-frequency bus. This indicates the AC voltage of the power frequency bus. Indicates the tap position of the on-load tap changer; function vector Characterize the nonlinear mapping relationship between the system power flow equations and the electrical response of key equipment; Based on the sensitivity matrix, the nonlinear equipment parameter relationships such as transformer impedance, converter valve loss, and submarine cable distributed parameters are approximated by piecewise linearization and mapped to a family of piecewise affine functions. ,in For the first The coefficient matrix of the segment, For the corresponding offset vector, This represents the total number of segments; By embedding a family of piecewise affine functions into the power feasible region constraints, a convex hull model containing mixed integer variables is constructed as the basic structure of the mathematical model.

[0014] In the preferred embodiment, an interval expansion and contraction iterative algorithm is used to perform robust boundary estimation of the uncertain parameters in the mathematical model, including: initializing the uncertain parameter interval. ,in and These represent the lower and upper bounds of the parameter, respectively. The output response range is obtained by performing forward propagation calculation. ,in and These are the minimum and maximum values ​​of the output, respectively. If the interval width Exceeding the preset tolerance Then, the input interval is bisected along the direction of maximum sensitivity in the sensitivity matrix, and each sub-interval is processed recursively until the output interval width of all sub-intervals satisfies the requirement. ; The robust boundary obtained after convergence is used as the input boundary condition for the sub-power circle calculation to ensure that the final determined power operating range covers the worst operating conditions under equipment parameter perturbation.

[0015] A flexible low-frequency transmission capacity analysis system for offshore wind power includes: The mathematical model building unit is used to establish a mathematical model of the equipment parameters and store the constraints. The sub-power circle acquisition unit is used to calculate each sub-power circle according to the mathematical model and the preset boundary combination; The power operating range calculation unit is used to take the intersection of sub-power circles of the same level and the union of power operating ranges of different levels, and output the complete power operating range.

[0016] This invention provides a method and system for capacity analysis of flexible low-frequency transmission systems for offshore wind power. By constructing a refined mathematical model integrating low-frequency bus voltage, reactive power, power frequency bus voltage, on-load tap changer positions, and key equipment parameters, and comprehensively considering multiple operational constraints such as modulation index, transformer capacity, valve-side voltage and current, and bridge arm current, this invention achieves a high-precision characterization of the power operating range of the flexible low-frequency transmission system for offshore wind power. The multivariate coupled sensitivity analysis, piecewise affine approximation, and convex envoy modeling methods employed effectively handle the nonlinear characteristics of the equipment and parameter uncertainties. Combined with the interval expansion-contraction iterative algorithm, this ensures that the obtained power boundary covers the worst-case operating conditions, significantly improving the reliability and robustness of the capacity analysis results. This method provides a clear technical basis for equipment selection, parameter optimization, and scheme comparison for flexible low-frequency transmission systems, helping to reduce engineering investment costs, improve submarine cable transmission capacity, and support stable system operation within a safe and efficient range, thereby promoting the large-scale application of flexible low-frequency transmission technology in medium- and long-distance offshore wind power transmission scenarios. Attached Figure Description

[0017] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a diagram of the flexible low-frequency power transmission system architecture in an embodiment of the present invention; Figure 2 This is a diagram illustrating the implementation steps of an embodiment of the present invention; Figure 3 This is a system architecture diagram in this embodiment of the invention. Detailed Implementation

[0018] Example 1 like Figure 1-2 As shown, a method for analyzing the flexible low-frequency transmission capacity of offshore wind power is provided. The method includes: A mathematical model is established that includes low-frequency bus AC voltage, low-frequency bus reactive power, power frequency bus AC voltage, on-load tap changer position and equipment parameters, and operational constraints such as modulation index, transformer capacity, valve side voltage, valve side current and bridge arm current are introduced. Based on the mathematical model, multiple sub-power circles are calculated for different boundary combinations and tap changer positions. The power operating range of a given range is obtained by taking the intersection of the sub-power circles under the same range and then taking the union of the power operating ranges of different ranges.

[0019] This method first constructs a comprehensive mathematical model. This model uses low-frequency bus AC voltage, low-frequency bus reactive power, power frequency bus AC voltage, on-load tap changer positions, and key equipment parameters as basic variables. It also incorporates multi-dimensional operational constraints such as modulation index, transformer capacity, valve-side voltage, valve-side current, and bridge arm current to comprehensively reflect the physical and engineering limitations faced by the flexible low-frequency transmission system in actual operation. Based on this model, by systematically combining the boundary values ​​of each variable and different on-load tap changer positions, corresponding sub-power circles are calculated. Each sub-power circle represents the feasible active and reactive power region where the system can operate safely under specific boundary conditions.

[0020] Subsequently, the method performs an intersection operation on all sub-power circles under the same tap changer position to obtain the conservative power operating range that satisfies all constraints under that position. Then, it performs a union and fusion of the power operating ranges corresponding to different positions to finally form a complete power operating boundary covering the full regulation capability. This process not only considers the static electrical constraints of the system but also fully incorporates the impact of operational flexibility on transmission capacity, thereby achieving a refined and high-fidelity analysis of flexible low-frequency transmission capacity.

[0021] This scheme accurately depicts the actual transmission capacity of offshore wind power flexible low-frequency transmission systems under complex operating conditions, avoiding capacity overestimation or equipment over-design due to simplified assumptions. It provides a reliable basis for system planning, equipment selection, and economic evaluation in the early stages of engineering projects. Simultaneously, the obtained power operating range can be directly used for operation scheduling strategy formulation and real-time monitoring, improving system safety margins and operating efficiency, and effectively supporting the engineering implementation and widespread application of flexible low-frequency power transmission technology in deep-sea wind power transmission.

[0022] In the preferred scheme, the regulation constraint is that the regulation m satisfies ,in and Determined by the characteristics of the converter valve.

[0023] The scheme introduces a modulation constraint, specifically requiring the modulation magnitude *m* to satisfy the inequality. The lower limit and upper limit It is not set arbitrarily, but is strictly determined based on the electrical characteristics of the converter valve, such as the device's withstand voltage, switching frequency limit, and modulation linearity range.

[0024] This constraint ensures that the modulation strategy is always within the safe and efficient operating range of the converter valve during system operation, avoiding insufficient voltage utilization due to excessively low modulation, or over-modulation, harmonic surges, or even device damage due to excessively high modulation.

[0025] By incorporating modulation constraints into the overall capacity analysis model, the method can accurately reflect the physical limitations of converter valves on the system's power regulation capability. This eliminates infeasible operating conditions when calculating the power operating range, improving the engineering applicability and reliability of the analysis results. This not only helps optimize converter design parameters but also prevents capacity misjudgments caused by neglecting modulation boundaries during the system planning stage, thereby improving the stability, economy, and feasibility of flexible low-frequency transmission systems.

[0026] In the preferred embodiment, the transformer capacity constraint includes: Calculate the lower boundary value of reactive power based on the assumption that the apparent power on the grid side does not exceed the rated capacity of the transformer. ; Calculate the upper boundary value of reactive power based on the assumption that the apparent power on the valve side does not exceed the rated capacity of the transformer. ; comprehensive and Determine the reactive power boundary q.

[0027] Network side view in power With rated capacity satisfy and active power With reactive power satisfy ; Valve side view in power With rated capacity satisfy and active power With reactive power satisfy .

[0028] This scheme uses dual lateral constraints to accurately characterize the impact of transformer capacity limitations on the system reactive power boundary. Specifically, firstly, based on the grid-side (i.e., power frequency side) operating conditions, it utilizes the fact that apparent power does not exceed the transformer's rated capacity. The principle, combined with grid-side voltage With current Relationship And based on active power With reactive power Satisfying the power circle equation The lower boundary value of reactive power that satisfies the safe operation of the grid side is derived. Similarly, on the valve side (i.e., the low-frequency side), based on the apparent power... and their corresponding power relationships Calculate the upper boundary value of the allowable reactive power on the valve side. Finally, by combining these two boundaries, the actual feasible reactive power range $q$ of the system is determined, ensuring that the transformer does not experience overload on either side.

[0029] This constraint mechanism fully considers the asymmetry and independence of the electrical characteristics of the transformers on both sides in flexible low-frequency transmission systems, avoiding misjudgments that may occur with traditional single-sided capacity verification. By modeling the capacity limitations on the grid side and the valve side separately and transforming them into explicit reactive power boundaries, the method significantly improves the accuracy and safety of capacity analysis. Its beneficial effects are twofold: firstly, it prevents transformer damage due to overload on one side, extending equipment life; secondly, it provides the system with a more realistic reactive power regulation margin, supporting converter control strategy optimization and reactive power compensation configuration, thereby improving the overall operating efficiency and reliability of the offshore wind power transmission system.

[0030] In the preferred embodiment, the valve-side voltage constraint is that the power frequency valve-side voltage does not exceed the maximum allowable value. , Valve-side current constraint: The power frequency valve-side current does not exceed the maximum allowable value. .

[0031] This scheme introduces hard limits on valve-side voltage and current, meaning the power frequency valve-side voltage must not exceed the maximum allowable value. The current on the power frequency valve side must not exceed the maximum allowable value. These limits are not theoretical assumptions, but rather directly derived from the electrical withstand capabilities and thermal stability requirements determined during the engineering design phase of the converter transformer, converter valve, and their connecting equipment. Specifically, The valve-side winding insulation class, partial discharge threshold, and overvoltage protection level are typically determined by a combination of these factors. This mainly depends on the current carrying capacity of the conductor material, heat dissipation conditions, and temperature rise limits under long-term operation. It is usually based on the rated continuous current and short-time overload capacity in the equipment nameplate parameters or type test report.

[0032] During the capacity analysis process, and As a boundary condition embedded in the mathematical model, it is used to screen feasible operating points: any power combination that causes the valve-side voltage or current to exceed the above limits is considered infeasible and thus excluded from the final power operating range. This constraint ensures that the system always operates within the equipment safety margin under various operating conditions, avoiding electrical breakdown caused by excessive voltage, or conductor overheating, device aging, or even burnout caused by excessive current.

[0033] By precisely introducing physical limits derived from actual equipment technical specifications, the engineering reliability and safety of the calculated transmission capacity are significantly improved. This not only helps to rationally match transformer and converter valve parameters during the planning stage, preventing the problem of "paper capacity" being far higher than the actual operational capacity, but also provides clear safety boundaries for real-time monitoring and scheduling during the operation stage, effectively supporting the reliable, efficient, and long-life operation of flexible low-frequency transmission systems in deep-sea wind power scenarios.

[0034] In the preferred embodiment, the arm current constraint is that the arm current does not exceed the maximum allowable value. .

[0035] The arm current constraint set in this scheme requires that the actual current of each arm of the converter in the flexible low-frequency transmission system must not exceed the maximum allowable value. This limit is directly derived from the thermal stability and electrical withstand capability of the power devices, submodule capacitors, bridge arm reactors, and internal connecting conductors in the modular multilevel converter. Specifically, Typically determined by the converter valve manufacturer based on the device junction temperature limit, heat dissipation design, short-term overload capacity, and long-term operational reliability tests, and clearly stated in the equipment technical specifications or type test report, these are the key boundary parameters for ensuring the safe operation of the converter valve.

[0036] During capacity analysis, this constraint is embedded in the mathematical model to assess whether the arm current is within a safe range under different power output conditions. Since the arm current is not only related to the transmitted power but also affected by modulation strategies, circulating current suppression effects, and frequency variations, its dynamic characteristics are more complex in flexible low-frequency systems. Therefore, it must be explicitly modeled and constrained. Any factor that causes the arm current to exceed... All operating points were deemed infeasible and were therefore eliminated from the final power operating range.

[0037] The introduction of this constraint significantly improves the accuracy of capacity analysis results in reflecting the physical limits of the converter itself, avoiding overestimation of capacity due to neglecting arm thermal stress or device current saturation. Its beneficial effects are twofold: firstly, it ensures that the converter valve parameters selected during the system design phase match the actual transmission requirements, preventing equipment overload risks; secondly, it provides clear current margin boundaries for control strategies, supporting the safe implementation of advanced functions such as circulating current suppression and power distribution, thereby enhancing the engineering feasibility, operational safety, and long-term reliability of the entire offshore wind power flexible low-frequency transmission system.

[0038] In the preferred scheme, the calculation of the sub-power circle includes: Multiple values ​​of the low-frequency bus AC voltage are selected within its minimum, maximum, and intermediate ranges. These values ​​are then combined with the boundary values ​​of the low-frequency bus reactive power, the boundary values ​​of the power frequency bus AC voltage, and different on-load tap changer positions and input into the mathematical model.

[0039] In this scheme, the calculation of the sub-power circle is achieved by systematically sampling the boundary and intermediate states of key operating variables. Specifically, firstly, the allowable range of the low-frequency bus AC voltage (including its minimum, maximum, and several intermediate values) is discretized; then, each voltage value is combined with the feasible boundary of the low-frequency bus reactive power, the operating limit of the power frequency bus AC voltage, and different on-load tap changer positions to form a multi-dimensional parameter combination set; finally, each set of parameters is substituted into the established mathematical model to solve for the active-reactive power pair that the system can safely transmit under the corresponding conditions, thereby generating a "sub-power circle" representing the feasible operating area under this specific operating condition.

[0040] This multi-parameter combination-based enumeration and calculation strategy is essentially a gridded partitioning method for the high-dimensional operating space. It can effectively capture the coupled effects of voltage level, reactive power support capability, grid-side voltage fluctuations, and transformer voltage regulation on the system's transmission capacity. Each sub-power circle reflects the local power feasible region under a certain set of boundary condition constraints, while the set of multiple sub-power circles together approximates the potential operating boundary of the entire system.

[0041] Its beneficial effects lie in the fact that by finely covering the range of changes in key variables, it avoids analytical biases caused by single-condition assumptions, significantly improving the comprehensiveness and robustness of power operating range calculations. This method can not only identify capacity bottlenecks under extreme conditions but also reveal the actual benefits of voltage regulation switching in improving transmission capacity, providing engineering design with decision-making basis closer to actual operating scenarios. Simultaneously, this structured calculation process facilitates subsequent integration with optimization algorithms or real-time monitoring systems, supporting the safe and efficient operation of flexible low-frequency transmission systems under complex sea conditions and grid conditions.

[0042] In the preferred embodiment, the steps for establishing a mathematical model that includes equipment parameters include: Constructing a multivariable coupled sensitivity matrix ; Wherein, the state vector , This indicates the low-frequency bus AC voltage. Indicates the reactive power of the low-frequency bus. This indicates the AC voltage of the power frequency bus. Indicates the tap position of the on-load tap changer; function vector Characterize the nonlinear mapping relationship between the system power flow equations and the electrical response of key equipment; Based on the sensitivity matrix, the nonlinear equipment parameter relationships such as transformer impedance, converter valve loss, and submarine cable distributed parameters are approximated by piecewise linearization and mapped to a family of piecewise affine functions. ,in For the first The coefficient matrix of the segment, For the corresponding offset vector, This represents the total number of segments; By embedding a family of piecewise affine functions into the power feasible region constraints, a convex hull model containing mixed integer variables is constructed as the basic structure of the mathematical model.

[0043] To construct the mathematical model, the state vector is first defined as follows: ; in This refers to the amplitude of the low-frequency bus voltage. Inject reactive power to the low-frequency side. The voltage amplitude is the power frequency side bus voltage, and t is the tap position of the on-load tap changer. Dimensionless integer. .

[0044] Function vectors The system of representation is given The electrical response under these conditions is specifically composed of the following four core equations: Low-frequency side power flow balance equation: ; in Active power output for wind farms The low-frequency side port voltage and phase angle of the converter. For equivalent connection reactance, For low-frequency bridge arm losses, it depends on and bridge arm current .

[0045] Reactive power constraint equations: ; 3. Valve-side voltage-gear mapping relationship: ; in The ratio function corresponding to tap position t is usually a piecewise constant or a step function.

[0046] Bridge arm current calculation equation: ; Based on the above set of nonlinear equations, a multivariable coupling sensitivity matrix is ​​constructed: ; This matrix reveals the local sensitivity of each state variable to the system response, and is especially useful for identifying strongly nonlinear regions.

[0047] Based on this, the transformer impedance , converter valve loss And the nonlinear relationship between submarine cable distributed parameters, etc., where the submarine cable distributed parameters are the resistance per unit length. ,inductance As the frequency f changes, an adaptive piecewise linearization strategy is adopted: the variable domain is divided into K sub-intervals based on the sensitivity mutation point or a preset error threshold; within each sub-interval k, the nonlinear function is approximated as an affine form. ; For example, submarine cable current carrying capacity The relationship between frequency f and laying temperature T can be linearized as follows:

[0048] Where the coefficient Determined by least squares fitting.

[0049] Finally, all piecewise affine expressions are embedded into the original constraint set, and binary variables are introduced. Representing the current working interval, construct a mixed-integer convex hull model: ; ; ; in M is a sufficiently large constant representing the nonlinear output to be approximated. This structure retains both nonlinear characteristics and convex optimization solvability.

[0050] To achieve robust capacity analysis of offshore wind power flexible low-frequency transmission systems under parameter uncertainties, this scheme employs the Interval Bisection and Contraction Algorithm to estimate the boundary parameters of the mathematical model. The core of this method lies in recursively subdividing the input space and combining forward propagation with a sensitivity-guided segmentation strategy to accurately approximate the worst-case boundary of the output response.

[0051] In the preferred embodiment, an interval expansion and contraction iterative algorithm is used to perform robust boundary estimation of the uncertain parameters in the mathematical model, including: initializing the uncertain parameter interval. ,in and These represent the lower and upper bounds of the parameter, respectively. The output response range is obtained by performing forward propagation calculation. ,in and These are the minimum and maximum values ​​of the output, respectively. If the interval width Exceeding the preset tolerance Then, the input interval is bisected along the direction of maximum sensitivity in the sensitivity matrix, and each sub-interval is processed recursively until the output interval width of all sub-intervals satisfies the requirement. ; The robust boundary obtained after convergence is used as the input boundary condition for the sub-power circle calculation to ensure that the final determined power operating range covers the worst operating conditions under equipment parameter perturbation.

[0052] First, initialize the interval of uncertain parameters. Assume there is a set of uncertain parameter vectors in the system. Examples include transformer impedance tolerance, changes in submarine cable thermal resistance with laying depth, and the dispersion of converter valve conduction voltage drop. Each parameter is assigned an initial range: ; in and These are the lower and upper bounds of the i-th parameter, respectively. The overall input interval is denoted as... .

[0053] Secondly, forward propagation is performed to calculate the output response interval. The input interval is substituted into the established mathematical model (including piecewise affine functions), and interval arithmetic is used to calculate a conservative estimate of the output quantity y's interval. For example, if the loss model of a certain submodule is in piecewise linear form... And current The corresponding loss range is: ; For non-monotonic functions, affine envelopes need to be used to improve accuracy.

[0054] Third, determine convergence and perform interval segmentation. Calculate the current output interval width. .like ( If a preset tolerance is required, then the input space needs to be refined. At this point, the sensitivity matrix needs to be calculated. Find out The largest dimension This refers to the parameter that has the most sensitive impact on the output. Then, the original interval is moved along... Two directions: ; The remaining parameter intervals remain unchanged, generating two new sub-hyperrectangles. For each sub-interval, forward propagation and convergence checks are recursively performed until all branches satisfy the condition. .

[0055] Finally, the output boundaries of all convergent sub-intervals are merged, and the global minimum and maximum values ​​are taken as the robust boundaries: ; This boundary covers the worst-case scenario under parameter perturbation and serves as the input constraint for calculating the sub-power circle.

[0056] Specific applications of piecewise linearization in key equipment parameters: Transformer impedance: Modeled as a function of tap position t and frequency f, fitted within the grid cells as: ; Converter valve losses: The plane is divided into triangular units, and within each unit: ; Submarine cable distributed parameters: Piecewise linearization of resistance per unit length on the logarithmic frequency axis: ; Through the above mechanism, this invention achieves high-fidelity modeling of the characteristics of complex nonlinear devices, and ensures a conservative and compact capacity boundary even under parameter perturbations through interval iteration, providing a decision-making basis for engineering design that combines safety and economy. A flexible low-frequency transmission capacity analysis system for offshore wind power includes: The mathematical model building unit is used to establish a mathematical model of the equipment parameters and store the constraints. The sub-power circle acquisition unit is used to calculate each sub-power circle according to the mathematical model and the preset boundary combination; The power operating range calculation unit is used to take the intersection of sub-power circles of the same level and the union of power operating ranges of different levels, and output the complete power operating range.

[0057] Example 2 Further explanation in conjunction with Example 1, such as Figure 1-3 As shown, the method for analyzing the flexible low-frequency transmission capacity of offshore wind power is as follows: Mathematical Model Establishment: A mathematical model was constructed, including low-frequency bus AC voltage, low-frequency bus reactive power, power frequency bus AC voltage, on-load tap changer positions, and various equipment parameters. This model describes the relationship between the power operating range of the flexible low-frequency transmission system and the aforementioned factors. The following constraints were fully considered when constructing the model: Regulation constraint: Ensure that the regulation parameter m meets a specific value range within the power operating range to guarantee the normal operation of the converter valve. For example, m should meet the following... ,in and These are the upper and lower limits of the modulation index determined based on the characteristics of the converter valve. Transformer capacity constraint: Within the operating power range, the apparent power must not exceed the transformer's rated capacity. Specifically, the boundary values ​​for reactive power are determined through the following steps: Based on the assumption that the reactive power on the grid side does not exceed the rated capacity of the transformer, the boundary value of reactive power is obtained. Assume the power at the network side is... Rated capacity is The grid-side voltage is The grid-side current is ,according to Combined with the power calculation formula It can be calculated , This refers to the active power on the grid side. Based on the assumption that the apparent power on the valve side does not exceed the rated capacity of the transformer, the upper boundary value of reactive power is obtained. Assume the power at the valve side is... Rated capacity is The valve-side voltage is The valve-side current is Similarly, we can obtain . Combining the above two steps, the boundary value q of reactive power under transformer capacity constraints is determined. Valve-side voltage constraint: Within the power operating range, ensure that the power frequency valve-side voltage does not exceed the allowable value Vmax. This is achieved through relevant circuit calculation formulas, such as those based on the power transfer formula. P is active power, V is voltage, and I is current. Using the power factor and parameters such as transformer turns ratio, the relationship between the valve-side voltage and other parameters is determined, thereby obtaining the power range under valve-side voltage constraints. Valve-side current constraint: Ensure that the power frequency valve-side current does not exceed the allowable value Imax within the power operating range. Based on the current distribution in the circuit and the rated current parameters of the equipment, determine the valve-side current constraint conditions, and thus obtain the corresponding power range. Arm current constraint: Within the power operating range, ensure that the arm current does not exceed the allowable value Iarm_max. By analyzing the topology and current flow path of the converter valve, and combining relevant circuit theory, the relationship between the arm current and other parameters is determined, thereby obtaining the power range under the arm current constraint condition. Obtaining Sub-Power Circles: For the low-frequency bus AC voltage, low-frequency bus reactive power, and power frequency bus AC voltage, different boundary combinations are selected and combined with different on-load tap changer positions. These are then substituted into the mathematical model described above to calculate each sub-power circle. For example, for the low-frequency bus AC voltage, its minimum value Vmin, maximum value Vmax, and several intermediate values ​​are taken and combined with different boundary values ​​of the low-frequency bus reactive power and power frequency bus AC voltage to calculate the corresponding sub-power circles. Determine the power operating range: Take the intersection of the sub-power circles under the same on-load tap changer position to obtain the power operating range under that position. Then, take the union of the power operating ranges under different on-load tap changer positions to obtain the complete power operating range of the flexible low-frequency transmission system. Offshore wind power flexible low-frequency transmission capacity analysis system Mathematical Model Construction Unit: This unit is responsible for establishing a mathematical model of the power operating range of the aforementioned flexible low-frequency transmission system and the relationship between the low-frequency bus AC voltage, low-frequency bus reactive power, power frequency bus AC voltage, on-load tap changer position, and equipment parameters. It also considers various constraints and stores this information in the system's database for subsequent calculations. Sub-power circle acquisition unit: Based on the mathematical model and constraints provided by the mathematical model construction unit, this unit selects different boundary combinations of low-frequency bus AC voltage, low-frequency bus reactive power and power frequency bus AC voltage and different on-load tap changer positions according to the preset value rules, performs data substitution and calculation, obtains each sub-power circle, and stores the data results of these sub-power circles in the database. Power operating range calculation unit: It reads sub-power circle data for the same on-load tap changer position from the database, performs intersection calculations to obtain the power operating range for that position. Then, it reads power operating range data for different on-load tap changer positions, performs union calculations, and finally obtains the power operating range of the flexible low-frequency transmission system. The results are then displayed on the system's operating interface for user viewing and analysis.

[0058] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for analyzing the flexible low-frequency transmission capacity of offshore wind power, characterized by: The method includes: A mathematical model is established that includes low-frequency bus AC voltage, low-frequency bus reactive power, power frequency bus AC voltage, on-load tap changer position and equipment parameters, and operational constraints such as modulation index, transformer capacity, valve side voltage, valve side current and bridge arm current are introduced. Based on the mathematical model, multiple sub-power circles are calculated for different boundary combinations and tap changer positions. The power operating range of a given range is obtained by taking the intersection of the sub-power circles under the same range and then taking the union of the power operating ranges of different ranges.

2. The method for analyzing the flexible low-frequency transmission capacity of offshore wind power according to claim 1, characterized in that: adjustment Institutional constraints are used to regulate institutional m to satisfy ,in and Determined by the characteristics of the converter valve.

3. The method for analyzing the flexible low-frequency transmission capacity of offshore wind power according to claim 1, characterized in that: The transformer capacity constraint includes: Calculate the lower boundary value of reactive power based on the assumption that the apparent power on the grid side does not exceed the rated capacity of the transformer. ; Calculate the upper boundary value of reactive power based on the assumption that the apparent power on the valve side does not exceed the rated capacity of the transformer. ; comprehensive and Determine the reactive power boundary q.

4. The method for analyzing the flexible low-frequency transmission capacity of offshore wind power according to claim 3, characterized in that: Network side view in power With rated capacity satisfy and active power With reactive power satisfy ; Valve side view in power With rated capacity satisfy and active power With reactive power satisfy .

5. The method for analyzing the flexible low-frequency transmission capacity of offshore wind power according to claim 1, characterized in that: Valve-side voltage constraint: The power frequency valve-side voltage shall not exceed the maximum allowable value. , Valve-side current constraint: The power frequency valve-side current does not exceed the maximum allowable value. .

6. The method for analyzing the flexible low-frequency transmission capacity of offshore wind power according to claim 1, characterized in that: The bridge arm current constraint is that the bridge arm current does not exceed the maximum allowable value. .

7. The method for analyzing the flexible low-frequency transmission capacity of offshore wind power according to claim 1, characterized in that: The calculation of the sub-power circle includes: Multiple values ​​of the low-frequency bus AC voltage are selected within its minimum, maximum, and intermediate ranges. These values ​​are then combined with the boundary values ​​of the low-frequency bus reactive power, the boundary values ​​of the power frequency bus AC voltage, and different on-load tap changer positions and input into the mathematical model.

8. The method for analyzing the flexible low-frequency transmission capacity of offshore wind power according to claim 1, characterized in that: The steps to establish a mathematical model that includes equipment parameters include: Constructing a multivariable coupled sensitivity matrix ； Wherein, the state vector , This indicates the low-frequency bus AC voltage. Indicates the reactive power of the low-frequency bus. This indicates the AC voltage of the power frequency bus. Indicates the tap position of the on-load tap changer; function vector Characterize the nonlinear mapping relationship between the system power flow equations and the electrical response of key equipment; Based on the sensitivity matrix, the nonlinear equipment parameter relationships such as transformer impedance, converter valve loss, and submarine cable distributed parameters are approximated by piecewise linearization and mapped to a family of piecewise affine functions. ,in For the first The coefficient matrix of the segment, For the corresponding offset vector, This represents the total number of segments; By embedding a family of piecewise affine functions into the power feasible region constraints, a convex hull model containing mixed integer variables is constructed as the basic structure of the mathematical model.

9. The method for analyzing the flexible low-frequency transmission capacity of offshore wind power according to claim 8, characterized in that: Also includes: The interval expansion and contraction iterative algorithm is used to perform robust boundary estimation of the uncertain parameters in the mathematical model, including: initializing the interval of uncertain parameters. ,in and These represent the lower and upper bounds of the parameter, respectively. The output response range is obtained by performing forward propagation calculation. ,in and These are the minimum and maximum values ​​of the output, respectively. If the interval width Exceeding the preset tolerance Then, the input interval is bisected along the direction of maximum sensitivity in the sensitivity matrix, and each sub-interval is processed recursively until the output interval width of all sub-intervals satisfies the requirement. ; The robust boundary obtained after convergence is used as the input boundary condition for the sub-power circle calculation to ensure that the final determined power operating range covers the worst operating conditions under equipment parameter perturbation.

10. A flexible low-frequency transmission capacity analysis system for offshore wind power, characterized in that: The method for analyzing the flexible low-frequency transmission capacity of offshore wind power according to any one of claims 1-9 includes: The mathematical model building unit is used to establish a mathematical model of the equipment parameters and store the constraints. The sub-power circle acquisition unit is used to calculate each sub-power circle according to the mathematical model and the preset boundary combination; The power operating range calculation unit is used to take the intersection of sub-power circles of the same level and the union of power operating ranges of different levels, and output the complete power operating range.

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