A method for coordinating and optimizing power frequency overvoltage of a multi-element heterogeneous power supply through a flexible direct current external transmission system

Abstract

The application provides a power frequency overvoltage coordination optimization method for a multi-element heterogeneous power source through a flexible DC external transmission system, and relates to the technical field of power system safety and stability control. The method comprises the following steps: a sending end system model containing wind power, photovoltaic power, energy storage, thermal power and a flexible DC converter station is constructed, a grid connection point is taken as a reactive power exchange boundary, short-time reactive power imbalance caused by different synchronization of dynamic responses of the converter station and multiple types of power sources after fault removal is analyzed, and an influence mechanism of control parameters on overvoltage is determined; control variables of each power source are uniformly modeled as a candidate parameter vector, an optimization model with voltage peak value, recovery time and waveform index as dictionary sequence optimization objectives is established, a total constraint violation amount and a comparison vector are defined; an outer optimizer is combined with time domain simulation to call iteratively, a parameter vector is iteratively optimized through an alpha evolutionary algorithm, and an optimal parameter combination is output. The application can inhibit power frequency overvoltage of the flexible DC sending end system, and improve the transient voltage safety level of the multi-element heterogeneous power source external transmission system.

Description

Technical Field

[0001] This application relates to the field of power system safety and stability control technology, and in particular to a method for coordinated optimization of power frequency overvoltage in a flexible DC transmission system with multiple heterogeneous power sources. Background Technology

[0002] With the concentrated development of large-scale new energy bases in deserts, Gobi, and wastelands, and the continuous growth in demand for large-capacity cross-regional power transmission, the adoption of flexible DC transmission, especially flexible DC transmission systems based on modular multilevel converters (MMC), to realize the collection and transmission of diverse and heterogeneous power sources such as wind power, photovoltaics, energy storage, and thermal power has become an important development direction for new power systems.

[0003] Compared to single-power-source transmission scenarios, the dynamic process of multiple heterogeneous power sources after AC-side fault clearance via flexible DC transmission systems is more complex. Flexible DC converter stations possess rapid active and reactive power regulation capabilities, but the response speed, limiting characteristics, and exit logic of power electronic interface power sources such as wind power, photovoltaics, and energy storage, as well as synchronous machine excitation systems, differ significantly during low-voltage ride-through, dynamic reactive power support, and fault recovery phases. When a fault is cleared or a severe disturbance occurs in DC power, the reactive power back-off of various devices is asynchronous, easily leading to short-term reactive power surplus on the sending-end critical bus and inducing power frequency overvoltage.

[0004] Existing power frequency overvoltage suppression methods mainly rely on adding external devices such as synchronous condensers, STATCOMs, and grid-type energy storage, or modifying the control logic. The former increases engineering investment, while the latter increases the complexity of the control system and the difficulty of parameter tuning. Furthermore, most existing parameter optimization methods still focus on single-type renewable energy sources, single control layers, or specific fault scenarios, making it difficult to consider the dynamic coupling relationship between flexible DC converter stations and multiple types of sending-end power sources. Therefore, it is necessary to propose a coordinated optimization method for power frequency overvoltage that can achieve collaborative optimization of control variables across multiple devices under joint simulation conditions. Summary of the Invention

[0005] This application provides a coordinated optimization method for power frequency overvoltage of multiple heterogeneous power sources in a flexible DC transmission system. It aims to solve the problems that power frequency overvoltage is prone to occur after AC side fault clearance in a flexible DC transmission system for multiple heterogeneous power sources, that existing methods are difficult to uniformly characterize the coupling effect of control variables between the flexible DC converter station and the sending end of multiple heterogeneous power sources, and that it is difficult to achieve efficient optimization under strong constraint co-simulation conditions.

[0006] This application provides a method for coordinating and optimizing power frequency overvoltage in a flexible DC transmission system using multiple heterogeneous power sources. The method includes: A sending-end system model is constructed, including wind farms, photovoltaic power stations, energy storage power stations, thermal power units, reactive power compensation devices, and flexible DC converter stations. The sending-end grid connection point PCC is used as the reactive power exchange boundary. The short-term reactive power imbalance caused by the asynchronous dynamic response between the flexible DC converter station and the multi-element heterogeneous power supply at the sending end after the AC side fault is cleared is analyzed. Based on the short-term reactive power imbalance, the influence mechanism of the sending-end power supply control parameters on the system power frequency overvoltage is determined. Based on the aforementioned influence mechanism, the control variables of the flexible DC converter station and the multi-heterogeneous power supply at the sending end are uniformly modeled as candidate parameter vectors. A dictionary-order optimization model is established with the goal of achieving the comprehensive optimal transient voltage response of the key bus, and the total constraint violation quantity and comparison vector are defined. The method employs a joint invocation of an outer optimizer and an inner time-domain simulation. The outer optimizer writes candidate parameter vectors into the controllers corresponding to the flexible DC converter station and the multi-element heterogeneous power supply at the sending end. Under preset fault conditions, time-domain simulation is performed, and the transient voltage response index of the key bus is extracted and fed back to the outer optimizer. The outer optimizer calculates the fitness of the candidate parameter vectors based on the lexicographical optimization model, the total constraint violation, and the comparison vector. Iterative updates of the candidate parameter vectors are performed using the α-evolutionary algorithm until the termination condition is met, at which point the candidate parameter vector with the best fitness is output as the optimal parameter combination.

[0007] Furthermore, taking the PCC (Power Generation Center) at the sending-end grid connection point as the reactive power exchange boundary, the short-term reactive power imbalance caused by the asynchronous dynamic response between the flexible DC converter station and the multi-element heterogeneous power source at the sending end after the AC side fault is cleared is analyzed, including: When a flexible DC converter station adopts an MMC rectifier station structure, the reactive power regulation on the AC side of the converter station, the total reactive power output of the equivalent power supply group at the sending end, and the reactive power of the parallel reactive power compensation branch satisfy the following relationship: in, This refers to the reactive power regulation of the MMC rectifier station on the AC side. This represents the sum of reactive power output from the equivalent power supply group at the sending end. The reactive power supplied to the PCC by the parallel reactive power compensation branch; After the AC-side fault is cleared, the reactive power absorption recovery of the flexible DC converter station is relatively delayed, and there is a delay in the dynamic reactive power support withdrawal of wind power, photovoltaic, and energy storage power sources, resulting in a short-term reactive power surplus at the PCC. The relationship between the reactive power mismatch at the PCC bus and the critical bus voltage is as follows: in, This is the voltage at the PCC bus. For the short-circuit capacity of the sending system, This represents the reactive power mismatch at the PCC bus.

[0008] Furthermore, the mechanism by which the sending-end power supply control parameters affect the system's power frequency overvoltage is determined based on the aforementioned short-term reactive power imbalance, including: Under the voltage orientation approximation, according to dq The voltage and current components on the AC side of the MMC in the coordinate system are used to represent the reactive power exchange of the MMC rectifier station as follows: in, and They are respectively dq AC voltage components of MMC in coordinate system; and They are respectively dq Current components in the coordinate system; For the outer loop of the rectifier-side AC voltage, a first-order filter is introduced for voltage measurement. Its filtering and error expressions are as follows: in, The first-order filter time constant for AC voltage measurement; This is the voltage outer loop proportional gain; The integral time constant for voltage control. This is the AC voltage reference value; This is the initial reactive current reference value; u ( t )for t The measured value of AC voltage on the rectifier side at any given time; u f ( t (This refers to the measured value of AC voltage) u ( t The filtered output value after first-order low-pass filtering; t It is a time variable; e u ( t )for t Constant AC voltage outer loop error; i q,ref ( t () is the output of the outer loop of AC voltage. q Shaft current reference value; e u ( τ (This refers to historical moments in the scoring process) The corresponding AC voltage error; τ It is an integral variable, and its value range is 0~ t ; For the inner current loop, its tracking error and control output are: in, For current-controlled proportional gain, The integral time constant for current control. This is the initial control variable; e i ( t )for t Intra-loop tracking error of the instantaneous current; i q ( t )for t The alternating current on the rectifier side at all times q Axial components; U aci ( t )for t The output control quantity of the inner loop PI controller at any given time; For photovoltaic power plants in grid-connected converter-type power supplies at the sending end, the photovoltaic side voltage filtering, reactive power reference value, and reactive power output meet the following requirements: in, The time constant for photovoltaic-side voltage filtering. This is the filtered AC voltage. This is the proportional coefficient for reactive power PI control. Add reactive power support gain for fault ride-through. This represents the dynamic reactive power support function triggered by voltage deviation; This is a reference value for reactive current on the photovoltaic side; q This refers to the per-unit control quantity for reactive power on the photovoltaic side. U ref This is the AC voltage reference value; U f,pv The voltage value is the first-order filtered value of the measured AC voltage on the photovoltaic side. Q PV The reactive power output of the photovoltaic field; i q,pv The actual output of the photovoltaic side q Shaft reactive current component; For wind farms in grid-connected converter-type power sources at the sending end, the reference value for reactive current on the wind power side satisfies: in, This is the proportional coefficient of the outer loop of the voltage PI converter. This is the voltage scaling factor supported by the fault ride-through current. This is the filtered terminal voltage. This is a reference value for reactive current on the wind power side. U f,wt The voltage value is the AC voltage measurement value on the wind turbine side after first-order filtering; For energy storage power stations in grid-connected converter-type power sources at the sending end, the relationship between reactive power channel filtering and voltage support on the energy storage side satisfies: in, The time constant for reactive power channel filtering. This is the AC voltage support ratio factor. Generated reactive power channels for grid-connected energy storage converters q Shaft reactive current reference value, This is the filtered AC voltage value obtained from the energy storage side measurement.

[0009] Furthermore, the candidate parameter vector is represented as: in, They represent the first i Individuals t The corresponding control parameters for flexible DC, wind power, photovoltaic, thermal power, and energy storage in this iteration. Indicates the first t During the nth iteration i The candidate parameter vector corresponding to each individual.

[0010] Furthermore, the lexicographical order optimization model is expressed as: in, The feasible region is defined by 'min', which is the minimum value function. x This is a candidate parameter vector; J ( x ) is the candidate parameter vector x The corresponding comprehensive optimization objective; lex is the lexicographical comparison identifier, that is, multiple optimization indicators are compared sequentially according to a preset priority, rather than using a weighted summation method; V pk ( x () represents the peak voltage. T rec ( x ( ) represents the recovery time; J s ( x ) represents the waveform indicator; The voltage peak value, recovery time, and waveform parameters are defined as follows: in, t c , t e These are the fault clearing time and the simulation termination time, respectively. This is the steady-state reference voltage before the fault. To restore the criterion bandwidth; This refers to the duration window during which the voltage first enters the allowable bandwidth near the reference voltage after a fault is cleared. and represents the weighting coefficients for the voltage deviation and fluctuation terms; max is the maximum value function. V ( t , x ) is the candidate parameter vector x Under the action t The voltage response of the critical bus at any given time; inf is the lower bound operation used to determine the earliest time when the voltage recovery criterion is met; To restore the time variable within the criterion duration window; After fault clearance The critical bus voltage value at any given moment.

[0011] Furthermore, the lexicographical order optimization model satisfies the following constraints: in, and These are the d-th control parameters. x d The lower and upper bounds, D The dimension of the parameter to be optimized; This is the upper limit of the allowable power frequency overvoltage for critical busbars; This is the time when the fault is cleared. This refers to the minimum critical bus voltage during the fault duration period. This is the lowest permissible voltage limit during a fault. The selected steady-state time interval after the fault, where, This represents the starting point of the steady-state time interval. This represents the end of the steady-state time interval; This is the upper limit of the allowable voltage recovery time; This represents the maximum deviation of the critical bus voltage relative to the reference steady-state voltage within the steady-state window after a fault. This is the allowable threshold for steady-state deviation after a fault.

[0012] Furthermore, the total constraint violation quantity φ ( x ) is defined as: in, λ 1. λ 2. λ 3. λ 4 and λ 5 represents the non-negative weight coefficients corresponding to each constraint violation.

[0013] Furthermore, the comparison vector Defined as: The comparison vector prioritizes feasible solutions over infeasible solutions, and within the feasible region, it prioritizes candidate parameter vectors with lower voltage peak values, shorter recovery times, and better waveform indicators.

[0014] Furthermore, the outer optimizer ranks the candidate parameter vectors based on the total constraint violation and the comparison direction, including: For the current candidate parameter vector x Under preset fault conditions, time-domain simulation is performed to extract the response curve of the key bus voltage changing with time, and the voltage peak, recovery time and waveform index are determined based on the response curve. Determine the current candidate parameter vector based on the constraints. x Whether a solution belongs to the feasible region is determined by whether it satisfies all constraints. If so, it is considered a feasible solution. The total constraint violation is... φ ( x If there are constraints that are not met or the simulation is not feasible, calculate the total constraint violation based on the corresponding constraint violation term and determine it as an infeasible solution. Based on the total constraint violation, a comparison vector is constructed, and a lexicographical order comparison rule is set. The lexicographical order comparison rule includes: according to the lexicographical order optimization model, the voltage peak value, recovery time, and waveform index are compared sequentially. If the voltage peak values ​​are not equal, the candidate parameter vector with the smaller voltage peak value has better fitness. If the voltage peak values ​​are equal, the recovery time is compared, and the candidate parameter vector with the shorter recovery time has better fitness. If the recovery time is also equal, the waveform index is compared, and the candidate parameter vector with the smaller waveform index has better fitness. Based on the defined lexicographical order comparison rules, the fitness of all candidate parameter vectors in the current population is sorted, where: The fitness of candidate parameter vectors that are judged as feasible solutions is better than the fitness of all candidate parameter vectors that are judged as infeasible solutions. Within the feasible solutions, sorting is performed according to the lexicographical order comparison rules to obtain the sorting result; Within an infeasible solution, the total constraint violation is compared first. The candidate parameter vector with the smaller total constraint violation has better fitness. If the total constraint violation is equal, the vectors are sorted according to the lexicographical order comparison rule to obtain the sorting result. The sorting results are used as the fitness evaluation results for each candidate parameter vector in the current population.

[0015] Furthermore, the method of iteratively updating the candidate parameter vector using the α-evolutionary algorithm includes... The update form of the α-evolutionary algorithm is determined as follows: in, These are the basis vectors used to determine the starting position of the current evolution; As the attenuation factor, Here is the perturbation matrix. For the random step size term; For adaptive step size term, and These represent the better and worse solutions sampled from the candidate solution set, respectively. For control vectors, This represents the Hadamard product. For the first t The middle generation i The current position vector of each candidate individual. The first one obtained after updating by the AE algorithm t +1st generation i The position vectors of the candidate individuals; The update form of the basis vector is as follows: in, For a sampling matrix with replacement, This means taking the diagonal elements of a matrix to form a vector; This is a sampling matrix without replacement; This is the normalized weight vector; and The learning rate; For the first The basis vectors are obtained based on the diagonal sampling path; For the first t +1 generation diagonal sampling path updated basis vector; For the first tThe basis vectors obtained based on the weighted aggregation path; For the first t +1 is the updated basis vector of the weighted aggregation path; rand is a random number that follows a uniform distribution in the interval [0,1] and is used to randomly select between the diagonal sampling path and the weighted aggregation path.

[0016] The expression for the attenuation factor is: Where FES is the current fitness evaluation count, MaxFES is the maximum fitness evaluation count, and exp is the natural exponential function; After each iteration, the updated candidate parameter vector is rewritten into the corresponding controllers of the flexible DC converter station and the sending-end multi-element heterogeneous power source, and time-domain simulation is performed. The new key bus voltage response curves are extracted to calculate the new fitness ranking results. After reaching the maximum number of fitness evaluations, the candidate parameter vector with the best ranking is output as the optimal parameter combination.

[0017] The method for coordinating and optimizing power frequency overvoltage in a flexible DC transmission system using a multi-heterogeneous power source provided in this application has at least the following beneficial effects: This application constructs a sending-end system model including wind power, photovoltaic, energy storage, thermal power, and a flexible DC converter station. Using the PCC grid connection point as the reactive power exchange boundary, it characterizes the analytical relationship between short-term reactive power imbalance and power frequency overvoltage caused by the asynchronous dynamic response of the flexible DC converter station and the multi-source heterogeneous power sources at the sending end after AC-side fault clearance. It also determines the influence mechanism of each power source control parameter on the system's power frequency overvoltage, providing a theoretical basis for subsequent parameter optimization. Under the determined influence mechanism, the control parameters of the flexible DC converter station and various power sources (wind, solar, energy storage, and thermal) are uniformly modeled as candidate parameter vectors. An optimization model is established with the peak voltage of the key bus, recovery time, and waveform rationality as the lexicographical optimization objectives. Combined with the total constraint violation, feasible solution priority is implemented, thus avoiding the artificial dependence on weight coefficients in the traditional weighted summation method and making the optimization results more objective and reasonable. The outer optimizer and inner time-domain simulation are jointly invoked, using the alpha evolution algorithm to iteratively update the candidate parameter vector. Through an update mechanism combining basis vector guidance, random step-size exploration, and adaptive step-size development, it meets the requirements for efficient global optimization in a high-dimensional, strongly nonlinear parameter space, while also considering the coordinated operation of control parameters for various power sources at the flexible DC converter station and the sending end. The final optimal parameter combination reduces short-term reactive power surplus at the PCC, suppresses peak power frequency overvoltages on critical buses, and shortens voltage recovery time, thereby improving the transient voltage safety level of the flexible DC transmission system with diverse heterogeneous power sources. Attached Figure Description

[0018] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0019] Figure 1 A flowchart of a method for coordinating and optimizing power frequency overvoltage of a multi-element heterogeneous power source through a flexible DC transmission system, provided in an embodiment of this application; Figure 2 A schematic diagram of the structure of a flexible DC power transmission system for multi-element heterogeneous power sources provided in the embodiments of this application; Figure 3 A schematic diagram of reactive power exchange between a rectifier station and a sending-end power source provided in an embodiment of this application; Figure 4 A schematic diagram of the co-simulation framework provided in the embodiments of this application; Figure 5 A flowchart of power frequency overvoltage coordination optimization provided in the embodiments of this application; Figure 6 This is a modified New England 39-node system topology diagram provided in the embodiments of this application; Figure 7 The key bus voltage response curves are shown for different schemes provided in the embodiments of this application.

[0020] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concepts of this application to those skilled in the art through reference to specific embodiments. Detailed Implementation

[0021] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0022] It should be noted that in the embodiments of this application, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of this application. However, it does not mean that the applicant has used or necessarily used the solution.

[0023] The technical solution of this application and how it solves the above-mentioned technical problems will be described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will be described below with reference to the accompanying drawings.

[0024] This application provides a method for coordinating and optimizing power frequency overvoltage in a flexible DC transmission system using multiple heterogeneous power sources. Figure 1 As shown, the method includes the following steps S10-S30.

[0025] S10: Construct a sending-end system model including wind farms, photovoltaic power stations, energy storage power stations, thermal power units, reactive power compensation devices, and flexible DC converter stations. Using the sending-end grid connection point PCC as the reactive power exchange boundary, analyze the short-term reactive power imbalance caused by the asynchronous dynamic response between the flexible DC converter station and the multi-element heterogeneous power sources at the sending end after the AC side fault is cleared. Based on the short-term reactive power imbalance, determine the influence mechanism of the sending-end power supply control parameters on the system's power frequency overvoltage.

[0026] In one exemplary embodiment, such as Figure 2 The diagram shown is a structural schematic of a flexible DC transmission system for multi-source heterogeneous power sources provided in this application embodiment. This system adopts a topology where multi-source heterogeneous power sources are aggregated at the sending end and transmitted via flexible DC. The rectifier-side AC bus serves as the sending-end grid connection point (PCC). Four types of power sources—wind farms, photovoltaic power stations, energy storage power stations, and thermal power units—are connected to the rectifier-side AC bus via step-up transformers. A reactive power compensation device is connected in parallel to the bus, collectively forming the sending-end power cluster. The rectifier-side AC bus connects to a modular multilevel converter (MMC) rectifier station, which is then connected to the receiving-end MMC inverter station via a flexible DC transmission line. The inverter station output is connected to the inverter-side AC bus, ultimately feeding into the receiving-end grid and supplying power to the load. Various power supply reactive power compensation devices at the sending end and the MMC rectifier station complete the exchange and balance of reactive power at the PCC bus. When a fault occurs on the AC side and is disconnected, there is a dynamic response difference between the reactive power support withdrawal speed of different types of power supplies and the reactive power absorption recovery speed of the MMC rectifier station. This difference will cause short-term reactive power imbalance at the PCC bus and induce power frequency overvoltage. Based on this system topology, the influence mechanism of the sending end power supply control parameters on the system power frequency overvoltage can be further analyzed.

[0027] This embodiment is based on Figure 2 The multi-element heterogeneous power source shown is transmitted through a flexible DC transmission system, which constructs a sending-end system model including a wind farm, a photovoltaic power station, an energy storage power station, a thermal power unit, a reactive power compensation device, and a flexible DC converter station. The flexible DC converter station preferably adopts an MMC rectifier station structure.

[0028] like Figure 3The diagram shown is a schematic of reactive power exchange between the rectifier station and the sending-end power source according to an embodiment of this application. Taking the sending-end grid connection point PCC as the reactive power exchange boundary, the reactive power regulation on the AC side of the converter station, the total reactive power output of the equivalent power source group at the sending end, and the reactive power of the parallel reactive power compensation branch satisfy the following relationship: in, This refers to the reactive power regulation of the MMC rectifier station on the AC side. This represents the sum of reactive power output from the equivalent power supply group at the sending end. The reactive power supplied to the PCC by the parallel reactive power compensation branch.

[0029] When an AC fault or disturbance occurs, the PCC bus voltage drops rapidly, and the flexible DC converter station and power sources such as wind and solar power successively enter low-voltage support or current-limiting control states, disrupting the reactive power distribution relationship of the system. After the fault is cleared, the sending-end system enters the recovery phase. At this time, the flexible DC converter station is affected by AC side current constraints and the transient adjustment process of the control system, resulting in a relatively lagging reactive power absorption recovery. It is difficult to provide reactive power regulation matching the voltage recovery process in a short period of time. At the same time, the dynamic reactive power support withdrawal of power sources such as wind power, photovoltaics, and energy storage has a certain delay, and the output change of parallel reactive power compensation devices is relatively limited, resulting in a short-term reactive power surplus at the PCC, which drives the bus voltage to rise rapidly and form a power frequency overvoltage. Essentially, this is a short-term reactive power imbalance problem caused by the asynchronous dynamic response of the flexible DC converter station and the multi-element heterogeneous power sources at the sending end after the fault. The equivalent relationship can be written as: in, This is the voltage at the PCC bus. For the short-circuit capacity of the sending system, This represents the reactive power mismatch at the PCC bus. After the AC side fault is cleared, if... If the voltage is positive for a short period of time, the critical bus voltage will rise rapidly and form a power frequency overvoltage.

[0030] Under the voltage-oriented approximation, the reactive power exchange of the MMC rectifier station can be further expressed as: in, and They are respectively dq AC voltage components of MMC in coordinate system; and They are respectively dq Current components in the coordinate system. The reactive power absorption capacity of MMC is mainly determined by the q-axis current component. Decide.

[0031] For the outer loop of the rectifier-side AC voltage, a first-order filter is introduced for voltage measurement. Its filtering and error expressions are as follows: in, The first-order filter time constant for AC voltage measurement; This is the voltage outer loop proportional gain; The integral time constant for voltage control. This is the AC voltage reference value; This is the initial reactive current reference value; u ( t )for t The measured value of AC voltage on the rectifier side at any given time; u f ( t () represents the measured value of AC voltage. u ( t The filtered output value after first-order low-pass filtering; t It is a time variable; e u ( t )for t Constant AC voltage outer loop error; i q,ref ( t () is the output of the outer loop of AC voltage. q Shaft current reference value; e u ( τ (This refers to historical moments in the scoring process) The corresponding AC voltage error; τ It is an integral variable, and its value range is 0~ t . Increase or By reducing the reactive power, the converter station can more easily and quickly generate reactive power absorption commands, thereby reducing the reactive power surplus of the sending-end system and suppressing power frequency overvoltage.

[0032] For the inner current loop, its tracking error and control output can be expressed as: in, For current-controlled proportional gain, The integral time constant for current control. This is the initial control variable; e i ( t )for tIntra-loop tracking error of the instantaneous current; i q ( t )for t The alternating current on the rectifier side at all times q Axial components; U aci ( t )for t The output control quantity of the inner loop PI controller at any given time. Increase or Reducing these parameters will help the actual reactive power absorption to track the outer loop commands more quickly.

[0033] For grid-connected converter-type power supplies at the sending end, the following equivalent relationship is preferred to characterize their reactive power support characteristics. Photovoltaic-side voltage filtering, reactive power reference value, and reactive power output satisfy: in, The time constant for photovoltaic-side voltage filtering. This is the filtered AC voltage. This is the proportional coefficient for reactive power PI control. Add reactive power support gain for fault ride-through. This represents the dynamic reactive power support function triggered by voltage deviation; This is a reference value for reactive current on the photovoltaic side; q This refers to the per-unit control quantity for reactive power on the photovoltaic side. U ref This is the AC voltage reference value; U f,pv The voltage value is the first-order filtered value of the measured AC voltage on the photovoltaic side. Q PV The reactive power output of the photovoltaic field; i q,pv The actual output of the photovoltaic side q Shaft reactive current component.

[0034] The reactive current reference value on the wind power side meets the following requirements: in, This is the proportional coefficient of the outer loop of the voltage PI converter. This is the voltage scaling factor supported by the fault ride-through current. This is the filtered terminal voltage. This is a reference value for reactive current on the wind power side. U f,wt The voltage value is the AC voltage measurement value on the wind turbine side after first-order filtering.

[0035] The relationship between reactive power channel filtering and voltage support on the energy storage side satisfies: in, The time constant for reactive power channel filtering. This is the AC voltage support ratio factor. Generated reactive power channels for grid-connected energy storage converters q Shaft reactive current reference value, This is the filtered AC voltage value obtained from the energy storage side measurement.

[0036] The mechanism by which sending-end power supply control parameters affect system power frequency overvoltage can be summarized as follows: Grid-connected converter-type power supply control parameters primarily affect the short-term reactive power surplus of the sending-end system by altering the establishment strength, exit speed, and recovery process of reactive power support after fault clearance. With parameters , , , and It is positively correlated with the parameter , The correlation is negative; the control parameters of the synchronous machine mainly affect the overvoltage process by changing the response speed of the excitation system to the terminal voltage deviation and the reactive power output regulation capability. With parameters It is positively correlated with the parameter It shows a negative correlation.

[0037] S20: Based on the influence mechanism, the control variables of the flexible DC converter station and the multi-heterogeneous power supply at the sending end are uniformly modeled as candidate parameter vectors. A dictionary order optimization model is established with the goal of achieving the comprehensive optimal transient voltage response of the key bus, and the total constraint violation quantity and comparison vector are defined.

[0038] To address the high-dimensional, highly nonlinear, and strongly constrained parameter optimization problem under co-simulation conditions, the control variables of the flexible DC converter station and the multi-element heterogeneous power supply at the sending end are uniformly modeled as a candidate parameter vector. In an exemplary embodiment, it is assumed that the first... t During the nth iteration i The parameter vector corresponding to each individual is written as: in, D The dimension of the parameters to be optimized. To reflect the collaborative parameter tuning characteristics of multi-element heterogeneous power sources, the following will be used. Classified by equipment / control level: in, They represent the firsti Individuals t The corresponding control parameters for flexible DC, wind power, photovoltaic, thermal power, and energy storage in this iteration. Indicates the first t During the nth iteration i The candidate parameter vector corresponding to each individual.

[0039] With the goal of achieving the optimal comprehensive transient voltage response of the key bus, a lexicographical optimization model prioritizing feasibility is established: in, To satisfy the feasible region of various safety constraints and simulation feasibility constraints, min is the minimum value function; x This is a candidate parameter vector; J ( x ) is the candidate parameter vector x The corresponding comprehensive optimization objective; lex is the lexicographical comparison identifier, that is, multiple optimization indicators are compared sequentially according to a preset priority, rather than using a weighted summation method; V pk ( x () represents the peak voltage. T rec ( x (This refers to the recovery time.) J s ( x ) represents the waveform index.

[0040] To avoid the reliance on human weighting in traditional weighted summation methods, this embodiment adopts a lexicographical comparison method to consider voltage peak value, recovery time, and waveform rationality in sequence.

[0041] The voltage peak value, recovery time, and waveform parameters are defined as follows: in, t c , t e These are the fault clearing time and the simulation termination time, respectively. The steady-state reference voltage before the fault. To restore the criterion bandwidth, This refers to the duration window during which the voltage first enters the allowable bandwidth near the reference voltage after a fault is cleared. and Here, represents the weighting coefficients for the voltage deviation and fluctuation terms, and max is the maximum value function. V ( t , x) is the candidate parameter vector x Under the action t The voltage response of the critical bus at any given time; inf is the lower bound operation used to determine the earliest time when the voltage recovery criterion is met; To restore the time variable within the criterion duration window; After fault clearance The critical bus voltage value at any given moment.

[0042] The lexicographical order optimization model simultaneously satisfies the following constraints: in, and These are the d-th control parameters. x d The lower and upper bounds, D The dimension of the parameter to be optimized; The upper limit of the allowable power frequency overvoltage for critical busbars is set to 1.1 pu in this embodiment; This is the time when the fault is cleared. This refers to the minimum critical bus voltage during the fault duration period. This is the lowest permissible voltage limit during a fault. The selected steady-state time interval after the fault, where, This represents the starting point of the steady-state time interval. This represents the end of the steady-state time interval; This is the upper limit of the allowable voltage recovery time; This represents the maximum deviation of the critical bus voltage relative to the reference steady-state voltage within the steady-state window after a fault. This is the allowable threshold for steady-state deviation after a fault.

[0043] To integrate constraint feasibility and multi-index response into the individual evaluation process, the total constraint violation and comparison vector are defined as follows: in, λ 1. λ 2. λ 3. λ 4 and λ5 represents the non-negative weight coefficients corresponding to each constraint violation. Through the above definition, feasible solutions are prioritized over infeasible solutions; within the feasible region, candidate solutions with lower peak voltage, shorter recovery time, and better waveform indicators are preferentially selected.

[0044] S30: The outer optimizer and inner time-domain simulation are jointly invoked. The outer optimizer writes the candidate parameter vector into the controllers corresponding to the flexible DC converter station and the multi-element heterogeneous power supply at the sending end. Under the preset fault conditions, the time-domain simulation is performed and the transient voltage response index of the key bus is extracted and fed back to the outer optimizer. The outer optimizer calculates the fitness of the candidate parameter vector according to the lexicographical optimization model, the total constraint violation, and the comparison vector. The candidate parameter vector is iteratively updated through the α evolution algorithm until the termination condition is met, and then the candidate parameter vector with the best fitness is output as the optimal parameter combination.

[0045] Step S30 aims to achieve coordinated optimization of power frequency overvoltage. For example... Figure 4 The diagram shows a schematic of the co-simulation framework provided in this application embodiment. The power frequency overvoltage coordination optimization process is based on a transient overvoltage coordination optimization framework jointly invoked by Python and PowerFactory. This transient overvoltage coordination optimization framework includes an outer optimization program, a co-invocation closed loop, and an inner simulation module. The outer optimization program is configured in the outer optimizer, which internally sets up three functional units: intelligent optimization algorithm, control parameter generation, and individual update and optimization. The intelligent optimization algorithm adopts the alpha evolution algorithm, outputting candidate parameter vectors through the control parameter generation unit; after receiving the simulation index returned by the inner layer, the outer optimization program calculates the fitness of each candidate parameter vector based on the lexicographical optimization model, the total constraint violation, and the comparison vector, and then completes the iterative update and selection of the population through the individual update and optimization unit. The co-invocation closed loop proceeds step by step in the order of parameter generation, model assignment, time-domain simulation, index extraction, and fitness feedback. The inner simulation module performs inner time-domain simulation, which includes three execution steps: control parameter writing, fault scenario simulation, and key response extraction. The candidate parameter vector output from the outer layer enters the closed loop and is then written to the corresponding controllers of the flexible DC converter station and the sending-end multi-element heterogeneous power supply through the model assignment stage. Fault scenario simulation is then performed under preset fault conditions, and time-domain calculations are completed. After the simulation, the key bus transient voltage response index is obtained through the key response extraction stage. After index calculation and fitness evaluation, the results are fed back to the outer optimization program. This closed-loop process iterates until a preset termination condition is met. The outer optimization program then outputs the candidate parameter vector with the best fitness as the optimal parameter combination, completing the coordinated optimization of power frequency overvoltage.

[0046] In an exemplary embodiment, the outer optimizer performs a merit-based ranking of candidate parameter vectors based on the total constraint violation and the comparison vector, including the following steps S301-S305.

[0047] S301: For the current candidate parameter vector x Under preset fault conditions, time-domain simulation is performed to extract the response curve of the key bus voltage changing with time, and the voltage peak, recovery time and waveform index are determined based on the response curve. S302: Determine the current candidate parameter vector based on the constraints. x Whether a solution belongs to the feasible region is determined by whether it satisfies all constraints. If so, it is considered a feasible solution. The total constraint violation is... φ ( x If there are constraints that are not met or the simulation is not feasible, calculate the total constraint violation based on the corresponding constraint violation term and determine it as an infeasible solution. S303: Based on the total constraint violation, construct a comparison vector and set a lexicographical order comparison rule; the lexicographical order comparison rule includes: according to the lexicographical order optimization model, compare the voltage peak value, recovery time, and waveform index in sequence. If the voltage peak values ​​are not equal, the candidate parameter vector with the smaller voltage peak value has better fitness; if the voltage peak values ​​are equal, compare the recovery time, and the candidate parameter vector with the shorter recovery time has better fitness; if the recovery time is also equal, compare the waveform index, and the candidate parameter vector with the smaller waveform index has better fitness. S304: Based on the set lexicographical order comparison rule, sort all candidate parameter vectors in the current population by fitness, wherein: the fitness of candidate parameter vectors judged as feasible solutions is better than the fitness of all candidate parameter vectors judged as infeasible solutions; within feasible solutions, sorting is performed according to the lexicographical order comparison rule to obtain the sorting result; within infeasible solutions, the total constraint violation is compared first, and the candidate parameter vector with the smaller total constraint violation is better in fitness; if the total constraint violation is equal, sorting is performed according to the lexicographical order comparison rule to obtain the sorting result. S305: Use the sorting results as the fitness evaluation results for each candidate parameter vector in the current population.

[0048] In one exemplary embodiment, a closed-loop approach combining outer-layer intelligent optimization and inner-layer time-domain simulation is employed. For any candidate parameter vector, the outer-layer optimization program first writes it into the corresponding controllers of the flexible DC converter station and the sending-end multi-element heterogeneous power supply; then, under preset fault conditions, time-domain simulation is performed to extract the peak voltage, recovery time, and waveform indicators of key bus, and feeds them back to the outer-layer optimizer to complete the fitness calculation.

[0049] The update form of the Alpha Evolution (AE) algorithm is as follows: in, These are the basis vectors used to determine the starting position of the current evolution; As the attenuation factor, Here is the perturbation matrix. This is a random step size term used to maintain population diversity and global exploration capabilities; For adaptive step size term, and These represent the better and worse solutions sampled from the candidate solution set, respectively. For control vectors, This represents the Hadamard product. For the first t The middle generation i The current position vector of each candidate individual. The first one obtained after updating by the AE algorithm t +1st generation i The position vectors of each candidate individual.

[0050] AE achieves coordination between exploration and development through a unified structure of basis vectors, random step size, and differential guided step size. Basis vectors It is adaptively generated from the sampling results of the evolution matrix through two evolution paths. One of them is a path based on diagonal sampling. The second is the path based on weighted aggregation. The corresponding update format can be written as: in, For a sampling matrix with replacement, This means taking the diagonal elements of a matrix to form a vector; This is a sampling matrix without replacement; This is the normalized weight vector; and The learning rate; For the first The basis vectors are obtained based on the diagonal sampling path; For the first t +1 generation diagonal sampling path updated basis vector; For the first t The basis vectors obtained based on the weighted aggregation path; For the first t +1 is the updated basis vector of the weighted aggregation path; rand is a random number that follows a uniform distribution in the interval [0,1] and is used to randomly select between the diagonal sampling path and the weighted aggregation path.

[0051] The random step size of AE is determined by the decay factor. and perturbation matrix Together, we determine that the decay factor decreases with the number of fitness evaluations, which is used to control the random step size to gradually transition from a larger search range in the early stage to a smaller local search range in the later stage.

[0052] Where FES is the current fitness evaluation count, MaxFES is the maximum fitness evaluation count, and exp is the natural exponential function.

[0053] After each iteration, the updated candidate parameter vector is rewritten into the corresponding controllers of the flexible DC converter station and the sending-end multi-element heterogeneous power source, and time-domain simulation is performed. The new key bus voltage response curves are extracted to calculate the new fitness ranking results. After reaching the maximum number of fitness evaluations, the candidate parameter vector with the best ranking is output as the optimal parameter combination.

[0054] In one exemplary embodiment, such as Figure 5 The diagram shown is a flowchart of the power frequency overvoltage coordination optimization provided in the embodiment of this application, which includes the following steps S310-S380.

[0055] S310: Set the control parameters to be optimized and their boundaries, and initialize the population and algorithm parameters; S320: Run-domain simulation, extracts key bus voltage response, calculates objective function and constraint violation, and finds the current global optimal solution; S330: Invoke the improved AE to update individual positions; execute Lévy flight perturbation on stationary individuals; S340: Import the updated parameter positions into the controller corresponding to the electromechanical transient simulation model for simulation; S350: Calculate the objective function and violation amount of the individual, and update the individual's position and the current optimal solution based on the constraint violation amount and the comparison vector; S360: Determine if the maximum fitness evaluation count has been reached; if not, return to step S330; if yes, proceed to the next step. S370: Outputs the optimal control parameters (i.e., the optimal parameter combination).

[0056] After the joint simulation optimization is completed, i.e., after step S30 is executed, the optimal parameter combination is written into the flexible DC converter station and the multi-element heterogeneous power controller at the sending end. After fault clearance, by improving the reactive power absorption and recovery speed of the MMC, optimizing the exit process of additional reactive power support during wind power and photovoltaic fault crossing, improving the tracking speed of the reactive power channel of the energy storage, and enhancing the ability of the synchronous machine excitation system to suppress the voltage deviation at the generator terminal, the short-term reactive power surplus at the PCC is reduced, thereby suppressing the power frequency overvoltage of the critical bus and shortening the voltage recovery time.

[0057] The feasibility and progressiveness of the method in this application will be further illustrated below with simulation verification.

[0058] This embodiment uses, as follows: Figure 6The modified New England 39-bus system shown verifies the method of this application. An ±800kV bipolar flexible DC transmission system is connected between nodes 2 and 25 of the standard New England 39-bus system, and a power supply cluster consisting of wind power, photovoltaic power, energy storage, and thermal power is connected at node 37, forming a multi-source heterogeneous power supply system transmitted via flexible DC.

[0059] like Figure 7 As shown in Table 1, under the same fault conditions, the initial peak overvoltage and recovery time of the critical bus 25 are 1.209 pu and 11.8 ms, respectively. After single-sided optimization using the AE algorithm, the peak overvoltage of the critical bus 25 is reduced to 1.134 pu, and the recovery time is shortened to 6.1 ms. After using the coordinated optimization method proposed in this invention, the peak power frequency overvoltage of the critical bus 25 is further reduced to 1.02 pu, and the recovery time is shortened to 1.0 ms.

[0060] Table 1 Simulation verification results of different schemes

[0061] The results above show that, under the same scenario, the method proposed in this application has a better optimization effect. The voltage of the key bus 25 after optimization is limited to below 1.1 pu and the recovery process is faster, indicating that the present invention can more effectively suppress the power frequency overvoltage of the flexible DC sending system.

[0062] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for coordinating and optimizing power frequency overvoltage in a flexible DC transmission system using multiple heterogeneous power sources, characterized in that, The method includes: A sending-end system model is constructed, including wind farms, photovoltaic power stations, energy storage power stations, thermal power units, reactive power compensation devices, and flexible DC converter stations. The sending-end grid connection point PCC is used as the reactive power exchange boundary. The short-term reactive power imbalance caused by the asynchronous dynamic response between the flexible DC converter station and the multi-element heterogeneous power supply at the sending end after the AC side fault is cleared is analyzed. Based on the short-term reactive power imbalance, the influence mechanism of the sending-end power supply control parameters on the system power frequency overvoltage is determined. Based on the aforementioned influence mechanism, the control variables of the flexible DC converter station and the multi-heterogeneous power supply at the sending end are uniformly modeled as candidate parameter vectors. A dictionary-order optimization model is established with the goal of achieving the comprehensive optimal transient voltage response of the key bus, and the total constraint violation quantity and comparison vector are defined. The method employs a joint invocation of an outer optimizer and an inner time-domain simulation. The outer optimizer writes candidate parameter vectors into the controllers corresponding to the flexible DC converter station and the multi-element heterogeneous power supply at the sending end. Under preset fault conditions, time-domain simulation is performed, and the transient voltage response index of the key bus is extracted and fed back to the outer optimizer. The outer optimizer calculates the fitness of the candidate parameter vectors based on the lexicographical optimization model, the total constraint violation, and the comparison vector. Iterative updates of the candidate parameter vectors are performed using the α-evolutionary algorithm until the termination condition is met, at which point the candidate parameter vector with the best fitness is output as the optimal parameter combination.

2. The method for coordinating and optimizing power frequency overvoltage in a flexible DC transmission system using multi-element heterogeneous power sources according to claim 1, characterized in that, Using the PCC (Power Generation Center) at the sending-end grid connection point as the reactive power exchange boundary, this paper analyzes the short-term reactive power imbalance caused by the asynchronous dynamic response between the flexible DC converter station and the multi-element heterogeneous power sources at the sending end after the AC side fault is cleared. This includes: When a flexible DC converter station adopts an MMC rectifier station structure, the reactive power regulation on the AC side of the converter station, the total reactive power output of the equivalent power supply group at the sending end, and the reactive power of the parallel reactive power compensation branch satisfy the following relationship: in, This refers to the reactive power regulation of the MMC rectifier station on the AC side. This represents the sum of reactive power output from the equivalent power supply group at the sending end. The reactive power supplied to the PCC by the parallel reactive power compensation branch; After the AC-side fault is cleared, the reactive power absorption recovery of the flexible DC converter station is relatively delayed, and there is a delay in the dynamic reactive power support withdrawal of wind power, photovoltaic, and energy storage power sources, resulting in a short-term reactive power surplus at the PCC. The relationship between the reactive power mismatch at the PCC bus and the critical bus voltage is as follows: in, This is the voltage at the PCC bus. For the short-circuit capacity of the sending system, This represents the reactive power mismatch at the PCC bus.

3. The method for coordinating and optimizing power frequency overvoltage in a flexible DC transmission system using multi-element heterogeneous power sources according to claim 2, characterized in that, The mechanism by which the sending-end power supply control parameters affect the system's power frequency overvoltage is determined based on the aforementioned short-time reactive power imbalance, including: Under the voltage orientation approximation, according to dq The voltage and current components on the AC side of the MMC in the coordinate system are used to represent the reactive power exchange of the MMC rectifier station as follows: in, and They are respectively dq AC voltage components of MMC in coordinate system; and They are respectively dq Current components in the coordinate system; For the outer loop of the rectifier-side AC voltage, a first-order filter is introduced for voltage measurement. Its filtering and error expressions are as follows: in, The first-order filter time constant for AC voltage measurement; This is the voltage outer loop proportional gain; The integral time constant for voltage control. This is the AC voltage reference value; This is the initial reactive current reference value; u ( t )for t The measured value of AC voltage on the rectifier side at any given time; u f ( t (This refers to the measured value of AC voltage) u ( t The filtered output value after first-order low-pass filtering; t It is a time variable; e u ( t )for t Constant AC voltage outer loop error; i q,ref ( t () is the output of the outer loop of AC voltage. q Shaft current reference value; e u ( τ (This refers to historical moments in the scoring process) The corresponding AC voltage error; τ It is an integral variable, and its value range is 0~ t ; For the inner current loop, its tracking error and control output are: in, For current-controlled proportional gain, The integral time constant for current control. This is the initial control variable; e i ( t )for t Intra-loop tracking error of the instantaneous current; i q ( t )for t The alternating current on the rectifier side at all times q Axial components; U aci ( t )for t The output control quantity of the inner loop PI controller at any given time; For photovoltaic power plants in grid-connected converter-type power supplies at the sending end, the photovoltaic side voltage filtering, reactive power reference value, and reactive power output meet the following requirements: in, The time constant for photovoltaic-side voltage filtering. This is the filtered AC voltage. This is the proportional coefficient for reactive power PI control. Add reactive power support gain for fault ride-through. This represents the dynamic reactive power support function triggered by voltage deviation; This is a reference value for reactive current on the photovoltaic side; q This refers to the per-unit control quantity for reactive power on the photovoltaic side. U ref This is the AC voltage reference value; U f,pv The voltage value is the first-order filtered value of the measured AC voltage on the photovoltaic side. Q PV The reactive power output of the photovoltaic field; i q,pv The actual output of the photovoltaic side q Shaft reactive current component; For wind farms in grid-connected converter-type power sources at the sending end, the reference value for reactive current on the wind power side satisfies: in, This is the proportional coefficient of the outer loop of the voltage PI converter. This is the voltage scaling factor supported by the fault ride-through current. This is the filtered terminal voltage. This is a reference value for reactive current on the wind power side. U f,wt The voltage value is the AC voltage measurement value on the wind turbine side after first-order filtering; For energy storage power stations in grid-connected converter-type power sources at the sending end, the relationship between reactive power channel filtering and voltage support on the energy storage side satisfies: in, The time constant for reactive power channel filtering. This is the AC voltage support ratio factor. The reactive power channel generated for the energy storage grid-connected converter q Shaft reactive current reference value, This is the filtered AC voltage value obtained from the energy storage side measurement.

4. The method for coordinating and optimizing power frequency overvoltage in a flexible DC transmission system using multi-source heterogeneous power sources according to claim 1, characterized in that, The candidate parameter vector is represented as follows: in, They represent the first i Individuals t The corresponding control parameters for flexible DC, wind power, photovoltaic, thermal power, and energy storage in this iteration. Indicates the first t During the nth iteration i The candidate parameter vector corresponding to each individual.

5. The method for coordinating and optimizing power frequency overvoltage in a flexible DC transmission system using multiple heterogeneous power sources according to claim 4, characterized in that, The lexicographical order optimization model is expressed as follows: in, The feasible region is defined by 'min', which is the minimum value function. x This is a candidate parameter vector; J ( x ) is the candidate parameter vector x The corresponding comprehensive optimization objective; lex is the lexicographical comparison identifier, that is, multiple optimization indicators are compared sequentially according to a preset priority, rather than using a weighted summation method; V pk ( x () represents the peak voltage. T rec ( x ( ) represents the recovery time; J s ( x ) represents the waveform indicator; The voltage peak value, recovery time, and waveform parameters are defined as follows: in, t c , t e These are the fault clearing time and the simulation termination time, respectively. This is the steady-state reference voltage before the fault. To restore the criterion bandwidth; The duration window during which the voltage first enters the allowable bandwidth near the reference voltage after a fault is cleared; and represents the weighting coefficients for the voltage deviation and fluctuation terms; max is the maximum value function. V ( t , x ) is the candidate parameter vector x Under the action t The voltage response of the critical bus at any given time; inf is the lower bound operation used to determine the earliest time when the voltage recovery criterion is met; To restore the time variable within the criterion duration window; After fault clearance The critical bus voltage value at any given moment.

6. The method for coordinating and optimizing power frequency overvoltage in a flexible DC transmission system using multi-element heterogeneous power sources according to claim 5, characterized in that, The lexicographical order optimization model satisfies the following constraints: in, and These are the d-th control parameters. x d The lower and upper bounds, D The dimension of the parameter to be optimized; This is the upper limit of the allowable power frequency overvoltage for critical busbars; This is the time when the fault is cleared. This refers to the minimum critical bus voltage during the fault duration period. This is the lowest permissible voltage limit during a fault. The selected steady-state time interval after the fault, where, This represents the starting point of the steady-state time interval. This represents the end of the steady-state time interval; This is the upper limit of the allowable voltage recovery time; This represents the maximum deviation of the critical bus voltage relative to the reference steady-state voltage within the steady-state window after a fault. This is the allowable threshold for steady-state deviation after a fault.

7. The method for coordinating and optimizing power frequency overvoltage in a flexible DC transmission system using multiple heterogeneous power sources according to claim 6, characterized in that, The total constraint violation φ ( x ) is defined as: in, λ 1. λ 2. λ 3. λ 4 and λ 5 represents the non-negative weight coefficients corresponding to each constraint violation.

8. The method for coordinating and optimizing power frequency overvoltage in a flexible DC transmission system using multi-source heterogeneous power sources according to claim 7, characterized in that, The comparison vector Defined as: The comparison vector prioritizes feasible solutions over infeasible solutions, and within the feasible region, it prioritizes candidate parameter vectors with lower voltage peak values, shorter recovery times, and better waveform indicators.

9. The method for coordinating and optimizing power frequency overvoltage in a flexible DC transmission system using multiple heterogeneous power sources according to claim 8, characterized in that, The outer optimizer ranks the candidate parameter vectors based on the total constraint violation and the comparison direction, including: For the current candidate parameter vector x Under preset fault conditions, time-domain simulation is performed to extract the response curve of the key bus voltage changing with time, and the voltage peak, recovery time and waveform index are determined based on the response curve. Determine the current candidate parameter vector based on the constraints. x Whether a solution belongs to the feasible region is determined by whether it satisfies all constraints. If so, it is considered a feasible solution. The total constraint violation is... φ ( x If there are constraints that are not met or the simulation is not feasible, calculate the total constraint violation based on the corresponding constraint violation term and determine it as an infeasible solution. Based on the total constraint violation, a comparison vector is constructed, and a lexicographical order comparison rule is set. The lexicographical order comparison rule includes: according to the lexicographical order optimization model, the voltage peak value, recovery time, and waveform index are compared sequentially. If the voltage peak values ​​are not equal, the candidate parameter vector with the smaller voltage peak value has better fitness. If the voltage peak values ​​are equal, the recovery time is compared, and the candidate parameter vector with the shorter recovery time has better fitness. If the recovery time is also equal, the waveform index is compared, and the candidate parameter vector with the smaller waveform index has better fitness. Based on the defined lexicographical order comparison rules, the fitness of all candidate parameter vectors in the current population is sorted, where: The fitness of candidate parameter vectors that are judged as feasible solutions is better than the fitness of all candidate parameter vectors that are judged as infeasible solutions. Within the feasible solutions, sorting is performed according to the lexicographical order comparison rules to obtain the sorting result; Within an infeasible solution, the total constraint violation is compared first. The candidate parameter vector with the smaller total constraint violation has better fitness. If the total constraint violation is equal, the vectors are sorted according to the lexicographical order comparison rule to obtain the sorting result. The sorting results are used as the fitness evaluation results for each candidate parameter vector in the current population.

10. The method for coordinating and optimizing power frequency overvoltage in a flexible DC transmission system using multiple heterogeneous power sources according to claim 9, characterized in that, The method of iteratively updating the candidate parameter vector using the alpha evolution algorithm includes: The update form of the α-evolutionary algorithm is determined as follows: in, These are the basis vectors used to determine the starting position of the current evolution; As the attenuation factor, Here is the perturbation matrix. For the random step size term; For adaptive step size term, and These represent the better and worse solutions sampled from the candidate solution set, respectively. For control vectors, This represents the Hadamard product. For the first t The middle generation i The current position vector of each candidate individual. The first one obtained after updating by the AE algorithm t +1st generation i The position vectors of the candidate individuals; The update form of the basis vector is as follows: in, For a sampling matrix with replacement, This means taking the diagonal elements of a matrix to form a vector; This is a sampling matrix without replacement; This is the normalized weight vector; and The learning rate; For the first The basis vectors are obtained based on the diagonal sampling path; For the first t +1 generation diagonal sampling path updated basis vector; For the first t The basis vectors obtained based on the weighted aggregation path; For the first t +1 is the updated basis vector of the weighted aggregation path; rand is a random number that follows a uniform distribution in the interval [0,1] and is used to randomly select between the diagonal sampling path and the weighted aggregation path. The expression for the attenuation factor is: Where FES is the current fitness evaluation count, MaxFES is the maximum fitness evaluation count, and exp is the natural exponential function; After each iteration, the updated candidate parameter vector is rewritten into the corresponding controllers of the flexible DC converter station and the sending-end multi-element heterogeneous power source, and time-domain simulation is performed. The new key bus voltage response curves are extracted to calculate the new fitness ranking results. After reaching the maximum number of fitness evaluations, the candidate parameter vector with the best ranking is output as the optimal parameter combination.

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