The application relates to a method for controlling the over-limit of terminal voltage of a power distribution network considering the static stable operation domain of a flexible on-load voltage regulating transformer

Abstract

This invention discloses a method for managing voltage exceedance at the end of a distribution network considering the static stability operating domain of a flexible on-load tap-changing transformer. Belonging to the technical field of distribution network voltage exceedance management, this method addresses the problems of voltage exceedance and equipment operating points easily approaching the stability boundary under high-proportion photovoltaic (PV) integration. The method involves: analyzing the voltage regulation mechanism of on-load tap changers and power electronic converters; constructing a static stability operating domain model and an equivalent turns ratio model based on P-V curves, and mapping operating slices to system-level variables; constructing a two-layer collaborative model using on-load tap changer positions, capacitor bank switching states, power electronic converter regulation, and PV inverter reactive power output as variables; establishing an objective function containing power flow balance and stable operating domain constraints, solving it, and applying the collaborative voltage regulation scheme to distribution network operation control. This invention suppresses voltage exceedance while ensuring that equipment operating points do not exceed the stability boundary, improving the coordination, precision, and safety of regulation.

Description

Technical Field

[0001] This invention relates to the field of distribution network voltage over-limit management technology, specifically to a distribution network end voltage over-limit management method that considers the static stability operating domain of flexible on-load tap-changing transformers. Background Technology

[0002] As the penetration rate of distributed photovoltaic (PV) power in distribution networks continues to increase, the operation mode of distribution networks is gradually shifting from traditional unidirectional power supply to bidirectional power flow interaction. Due to the randomness and volatility of PV output and its mismatch with load demand timing, the power flow distribution of distribution networks is becoming increasingly complex, which can easily lead to problems such as local voltage exceeding the upper limit at PV grid-connected nodes, low voltage at feeder end nodes, and aggravated node voltage fluctuations. These issues seriously affect the power supply quality, PV absorption capacity, and equipment operation safety of the distribution network.

[0003] To address the aforementioned voltage exceedance issue, existing technologies primarily employ on-load tap changers (OLTCs), parallel capacitor banks, and reactive / active power regulation of photovoltaic inverters. However, OLTCs rely on mechanical tap switches for discrete tap adjustment, resulting in low adjustment accuracy, slow response speed, and limited tap switch operation frequency due to mechanical lifespan constraints, making it difficult to mitigate frequent voltage fluctuations caused by high-proportion photovoltaic grid connections. Parallel capacitor banks can only perform discrete reactive power compensation through group switching, resulting in coarse-grained adjustment. The reactive power regulation capability of photovoltaic inverters is constrained by the remaining capacity of their converters; while reducing active power output can suppress voltage exceedances, it reduces photovoltaic power generation revenue and grid integration levels.

[0004] Flexible on-load voltage regulating transformers (FOVRTs) are a new type of voltage regulating device that combines the discrete coarse adjustment capability of traditional on-load tap changers with the continuous fine adjustment capability of power electronic converters (PECs). They have advantages such as a large voltage regulation range, fast response speed, and high regulation accuracy, and can, to a certain extent, make up for the shortcomings of the above-mentioned traditional voltage regulation methods and improve the voltage regulation capability of the distribution network. Reference [1] (LEE HJ, YOON SW, YOON Y D. Hybrid distribution transformer based on an existing distribution transformer and a series-connected power converter[J]. IEEE Transactions on Power Delivery, 2022, 37(5): 4202-4211.) discloses a hybrid distribution transformer based on an existing distribution transformer and a series-connected power converter, which combines the capacity advantage of mechanical voltage regulation with the continuous regulation advantage of power electronic voltage regulation; Reference [2] (HANL, YIN J, WU L, et al. Research on the novel flexible on-load voltage regulator transformer and voltage stability analysis[J]. Energies, 2022, 15(17): 6189.) further discloses a topology and voltage regulation control strategy of FOVRT, and verifies its effectiveness in improving the voltage level of the distribution network.

[0005] However, existing research on FOVRT still has the following shortcomings: Firstly, existing research mainly focuses on the topology, local control strategies, and basic voltage regulation characteristics of FOVRT, such as the technical solutions disclosed in references [1] and [2]. However, the static stable operating boundary formed by the combined action of OLTC discrete adjustment and PEC continuous compensation is not sufficiently characterized. As can be seen from the characteristics of the PV curve, there is a corresponding maximum transmittable power limit under each operating condition, namely the nose point of the PV curve. After the operating point crosses the nose point, there is no stable voltage solution in the system, and the voltage regulation capability of the voltage regulating device is constrained by the downstream transmittable power level. Although reference [3] (POMPODAKIS EE, KRYONIDIS GC, ALEXIADIS MC. A comprehensive three-phase step voltage regulator model with efficient implementation in the Z-bus power flow[J]. Electric PowerSystems Research, 2021, 199: 107443.) discloses a refined three-phase power flow model for step voltage regulators, which improves the modeling accuracy of voltage regulating equipment in power flow calculation, it only models the discrete tap characteristics of mechanical regulating equipment and does not involve the characterization of the stable operating domain under the coupling effect of discrete taps and continuous power electronic compensation. Therefore, the existing technology cannot accurately define the safe and feasible range of PEC compensation amount under different OLTC taps.

[0006] Secondly, in the process of system-level coordinated voltage regulation, most of the existing voltage management schemes follow the modeling ideas of reference [3], simply equating the voltage regulation equipment with an adjustable voltage source, or only applying upper and lower limits of the turns ratio to it before participating in optimization. They do not include the static stable operating domain of FOVRT, which is jointly determined by the characteristics of the PV curve and the equipment capacity, as a physical constraint in the coordinated voltage regulation optimization. This can easily lead to excessive PEC compensation action or even saturation, unclear division of labor between discrete regulation resources and continuous regulation resources, and even cause the equipment operating point to approach the stable boundary represented by the nose point of the PV curve, affecting the safe and stable operation of the equipment.

[0007] Therefore, how to combine the characterization of the FOVRT static stable operating domain with the collaborative voltage regulation optimization of multiple devices in the distribution network, and rationally allocate the regulation tasks of regulation resources such as OLTC, PEC, capacitor banks and photovoltaic inverters, and achieve voltage over-limit management at the end of the distribution network while ensuring that the equipment operating point does not approach the static stability boundary, is a technical problem that urgently needs to be solved to improve the voltage quality and operational stability of the distribution network in high-proportion photovoltaic access scenarios. Summary of the Invention

[0008] To address the issues of voltage exceeding limits at the distribution network end under high-proportion distributed photovoltaic (PV) grid integration and the tendency for the operating point of flexible on-load tap changers (FOVRTs) to approach the static stability boundary, this invention provides a method for mitigating voltage exceeding limits at the distribution network end, considering the static stability operating domain of FOVRTs. This method embeds the FOVRT static stability operating domain, constructed based on the PV curve, as a safety constraint into a discrete-continuous two-layer collaborative optimization model containing on-load tap changers (OLTCs), capacitor banks, power electronic converters (PECs), and PV inverters. This approach ensures that the equipment operating point does not exceed the stability boundary represented by the nose point of the PV curve, improves the nose point margin, and suppresses PEC saturation and boundary triggering. It also achieves a clear division of labor between discrete coarse adjustment and continuous fine adjustment, and the coordinated use of multiple adjustment resources. This effectively suppresses node voltage exceeding limits, reduces the maximum system voltage deviation, and improves the coordination, precision, and operational safety of distribution network voltage regulation.

[0009] The technical solution adopted in this invention is as follows: The method for mitigating voltage exceedance at the distribution network end in the static stability operating domain of flexible on-load tap-changing transformers includes the following steps: S1: Analyze the steady-state operation mechanism of flexible on-load tap-changing transformers and establish the coordinated tap-changing relationship between discrete tap changer adjustment and continuous compensation of power electronic converter; S2: Based on the coordinated voltage regulation relationship of S1, construct the static stable operation domain model and equivalent turns ratio model of the flexible on-load tap-changing transformer, and obtain the stable operation slices under each on-load tap-changing switch position. S3: Map the static stable operating domain to the distribution network system layer variables and establish the correspondence between the local operating quantities of the flexible on-load tap-changing transformer and the operating quantities at the head end of the distribution network; S4: Based on the correspondence in S3, construct a multi-device collaborative voltage over-limit management model, taking the on-load tap changer position and capacitor bank switching status as discrete control variables, and the power electronic converter regulation and photovoltaic inverter reactive power output as continuous control variables, and determine the constraints of each control variable. S5: Based on the constraints in S4, establish the objective function and apply power flow balance constraints and static stability operating domain constraints to obtain the distribution network voltage over-limit management optimization model; S6: Solve the distribution network voltage over-limit management optimization model to obtain the coordinated voltage regulation scheme; S7: Apply the coordinated voltage regulation scheme to the operation control of the distribution network to achieve the management of voltage over-limit at the end of the distribution network.

[0010] S1 includes: S1.1: Establish the voltage relationship between the primary and secondary sides of the flexible on-load tap-changing transformer: ; In the formula: This is the equivalent voltage of the upstream power supply referred to the secondary side; This is the secondary side voltage; , These are the equivalent active power and equivalent reactive power downstream of the output side of the flexible on-load tap-changing transformer, respectively. , These are the sum of the equivalent resistances and the sum of the equivalent reactances of the line and the power electronic converter, respectively. The imaginary unit; S1.2: Separate the real and imaginary parts of the voltage relationship in S1.1, and eliminate the phase difference by squaring. Later, we obtained information about The fourth equation, and then the load power factor relationship Substituting the values ​​into the equation, we obtain the PV relationship between the secondary voltage and active power: ; In the formula: for and The phase difference between them; This refers to the phase angle between the load-side voltage and current. This is the sum of the equivalent impedances of the line and the power electronic converter; To solve for intermediate variables; The equivalent active power is The corresponding secondary voltage at that time.

[0011] S2 includes: S2.1: Based on the PV relation obtained in S1.2, let... Transform it into a quadratic equation in one variable: ; Where: is the criterion for the existence of a stable voltage solution in the system. Determine the active power limit corresponding to the nose point of the PV curve; To replace the variable, ; The coefficient of the linear term; For constant terms; For transformer turns ratio; S2.2: Within the active power limit range determined in S2.1, establish the equivalent turns ratio of the power electronic converter. and its adjustment range Based on this, a stable operation slice under a fixed on-load tap changer position is constructed. ,Right now And it satisfies: ; ; ; In the formula: Compensation voltage injected into the power electronic converter; This is the difference in turns ratio between two adjacent on-load tap changer positions. This is the on-load tap changer position; For the first The active power limit corresponding to the nose point of the PV curve at each gear level; For gear position number; , Given respectively The lower and upper boundaries of the stable operating voltage; S2.3: Determine the voltage regulation mode switching conditions based on the stable operation slice constructed in S2.2: when and At that time, continuous adjustment is performed by the power electronic converter; when And the running point is close At the boundary, the on-load tap changer is triggered to switch from the tap position. Adjust to Subsequently, the power electronic converter re-entered a small-range regulation; and an equivalent turns ratio model for the flexible on-load tap-changing transformer was established: ; In the formula: This is the equivalent turns ratio of a flexible on-load tap-changing transformer.

[0012] S3 includes: S3.1: Install a flexible on-load tap-changing transformer between upstream power supply node 0 and distribution network head-end node 1 to convert the output voltage in the local model. This corresponds to the voltage of node 1 in the system layer. , Number the scheduling period; S3.2: Based on the voltage correspondence established in S3.1, the equivalent active power in the local model is... Equivalent reactive power These correspond to the active power flow sent downstream from the branch of node 0 to node 1 to the distribution network. and the trend of no effort ; S3.3: Based on the variable correspondence established in S3.1 and S3.2, adjust the on-load tap changer positions in the static model. Equivalent turns ratio of power electronic converter Expanded to time period variables and This makes the statically stable operating domain constraints express as: ; In the formula: Gear position at time t The corresponding stable running slice.

[0013] In S4, the constraints on the discrete control variables include: S4.1: Establish capacitor bank switching constraints: ; ; ; In the formula: The node at time t i The number of capacitor banks put into operation; This is the maximum number of capacitor banks that can be connected. The node at time t i The reactive power provided by the capacitor bank; This refers to the rated capacity of a single capacitor bank. , These are 0-1 variables representing the increase or decrease in the number of capacitor banks being put into operation; This is the maximum number of times a capacitor bank can be switched on and off per day. For the set of scheduling periods; Number the nodes; S4.2: Based on the discrete reactive power compensation capability determined in S4.1, establish on-load tap changer position constraints: ; ; In the formula: , These are the minimum and maximum positions of the on-load tap changer, respectively. This is an indicator function, taking the value 1 if the condition is true and 0 otherwise; This represents the maximum number of file transfers allowed per day.

[0014] In S4, the constraints on the continuous control variables include: S4.3: Establish reactive power output constraints for photovoltaic inverters: based on the photovoltaic grid connection point voltage. With voltage reference point , , , , The reactive power output of the photovoltaic inverter is determined by segmenting the relative positions. And its maximum available reactive power capacity is: ; In the formula: The apparent power capacity of the photovoltaic inverter; Let be the photovoltaic active power output of node i at time t; , , , , These are the five voltage reference points for the segmented control of the photovoltaic inverter; S4.4: Within the reactive power regulation capability boundary determined in S4.3, establish a voltage regulation model for the power electronic converter: ; In the formula: for t Equivalent transformation ratio at time; for t The equivalent turns ratio adjustment of the power electronic converter at any time; This represents the maximum permissible change in the equivalent ratio adjustment between adjacent time periods; , They are respectively t The active and reactive power delivered downstream by the interface branch of the flexible on-load tap-changing transformer at all times; for t Voltage at the beginning node of the distribution network at all times; for t The current amplitude of the interface branch at that time. Its conjugate; for t The equivalent voltage of the upstream power supply is calculated to the secondary side at all times; , These are the equivalent active power component and reactive power component of the power electronic converter, respectively. The apparent power capacity of the power electronic converter; , These are operations for taking the imaginary part and the real part, respectively.

[0015] S5 includes: S5.1: Establish power flow balance constraints: ; In the formula: , Branch roads ij Active and reactive power; For downstream node indexing; For the set of line nodes; , These are the active and reactive power of the load, respectively. , These represent the active and reactive power losses of the branch circuits, respectively. , These are the branch resistance and reactance, respectively. Number the nodes; Let j be the voltage at node j; This represents the amplitude of the branch current.

[0016] S5.2: Based on the power flow balance constraints established in S5.1, the static stable operating domain constraints are embedded as shared coupling constraints between discrete and continuous control variables: ; S5.3: Establish the objective function under the constraints of S5.1 and S5.2: ; ; ; ; In the above formula: The objective function is for the discrete layer. For continuous layer objective function; This is a penalty item for voltage exceeding the limit; This is the cost of file retrieval; For the cost of cutting; , These are the lower and upper voltage limits for node i, respectively; , , The weights of each component in the discrete layer; This refers to network losses. This is a continuously adjusting resource utilization rate item; To adjust the smoothness term; , , These represent the weights of each component in the continuous layer.

[0017] The S6 algorithm employs a fuzzy triple black hole algorithm for solution, including: S6.1: Employs double-layer nested encoding: Outer particles only encode discrete control variables ; Continuous control variables It does not participate in the outer layer encoding and is solved independently by the inner layer after the outer layer particles are given. In the formula: This is the gear timing vector; This is the switching state matrix for the capacitor bank; This is the equivalent variable ratio adjustment vector; This is the reactive power compensation timing vector; This is the reactive power output matrix for a photovoltaic inverter. This is a vectorization operation performed by expanding by row; , These are the particle number and the number of iterations, respectively. , These are the discrete layer and continuous layer encoding vectors, respectively. S6.2: Randomly generate initial positions for particles encoded in S6.1 according to the upper and lower bounds of the variables: Based on the initial velocity, and to repair the updated particles: Discrete variables by Rounding and repair, continuous variables according to Boundary truncation repair; In the formula: Number the particles; Number the dimensions; This represents the number of iterations. , These are the upper and lower bounds of the d-th dimension variable, respectively; is a random number uniformly distributed in the interval [0,1]. It is a rounding function; S6.3: For each outer layer particle after S6.2 repair, the inner layer aims to minimize the continuous layer objective function, solve for the optimal value of the continuous control variable, and then use the discrete layer objective function value, the continuous layer objective function value and the constraint violation penalty term as weights to form the comprehensive fitness; S6.4: Based on the comprehensive fitness obtained in S6.3, update the individual optimal position and the global optimal position, use the triple black hole mechanism to update the particle position, and perform mutation on the particle with the mutation probability determined by fuzzy control. After iterating to convergence, output the cooperative voltage regulation scheme.

[0018] In S6.3, the overall fitness is: ; ; In the formula: , These are the objective function values ​​for the discrete layer and the continuous layer, respectively. These are the weighting coefficients for each item; ; ; ; ; In the formula: This is a penalty item for voltage exceeding the limit; This is a penalty item for statically stable operating domains. , Given time t The lower and upper voltage limits allowed in the lower static stable operating domain; As a penalty for mismatch with trends, , These are the active power flow balance residuals and reactive power flow balance residuals of node i at time t, respectively. This is a penalty item for exceeding the limit without performing any work. Let t be the upper limit of the reactive power output of the power electronic converter. This refers to the set of nodes connected to the photovoltaic inverter.

[0019] S6.4 includes: S6.4.1: Setting the center of three types of black holes: ; In the formula: Let be the globally optimal particle position in the q-th iteration; , These are the upper and lower bound vectors of the search space, respectively; S6.4.2: Based on the black hole center setting in S6.4.1, when the particle is outside the black hole's influence range, update the particle velocity and position using the following formula: ; When a particle enters the black hole's influence range, a capture update or escape update is performed according to the confidence strategy. In the formula: Inertial weight; , These are individual learning factors and group learning factors, respectively. , A random number in the interval [0,1]; The optimal position for the individual; S6.4.3: Based on the position update in S6.4.2, adjust the mutation probability according to fuzzy control. Perform mutation updates on particles that meet the mutation conditions: ; And adaptively update the inertia weights and learning factors according to the following formula: ; In the formula: For fuzzy controller mapping functions; , , These are the current population's optimal fitness value, fitness standard deviation, and fitness fluctuation value, respectively. Let be the variable-length coefficient of the d-th dimension variable; A random number in the interval [0,1]; , These are the upper and lower limits of the inertia weight, respectively; , These are the upper and lower limits of the individual learning factor, respectively; , These are the upper and lower limits of the group learning factor, respectively. This represents the maximum number of iterations.

[0020] This invention provides a method for mitigating voltage exceedance at the end of a distribution network, considering the static stability operating domain of flexible on-load tap-changing transformers. The technical advantages are as follows: 1) This invention constructs a static stable operating domain model and an equivalent turns ratio model for a flexible on-load tap-changing transformer based on the characteristics of the PV curve. By determining the power limit represented by the nose point of the PV curve at each tap position using the criterion of the existence of a stable voltage solution, a tap-by-taper stable operating slice is formed. Compared with existing technologies that only focus on topology, local control strategies, and basic voltage regulation characteristics, this invention, for the first time, clearly defines the safe and feasible operating range of the equipment under the combined action of discrete tap-changing and continuous compensation. This solves the problem of insufficient characterization of the static stable operating boundary in the background technology and provides a clear physical constraint basis for the equipment to participate in distribution network system-level voltage regulation.

[0021] 2) This invention embeds the static stable operating domain constraint as a shared coupling constraint between the discrete and continuous layers into the collaborative voltage regulation optimization, ensuring that the operating point at the beginning of the flexible on-load tap-changing transformer maintains a safety margin relative to the stability boundary represented by the nose point of the PV curve at all time periods. Compared with existing technologies that merely equate the voltage regulating equipment to an adjustable voltage source or only apply upper and lower limits of the turns ratio, this invention effectively suppresses excessive or even saturated compensation actions of the power electronic converter, preventing the equipment operating point from approaching the unstable region and solving the safety hazards caused by ignoring the stable operating domain constraint in system-level voltage regulation in the background technology.

[0022] 3) This invention reconstructs the voltage regulation division of labor within a flexible on-load tap-changing transformer by switching between continuous regulation within a stable operating slice and discrete tap-changing triggered by the slice boundary: the on-load tap changer undertakes the phased setting of the voltage reference, while the power electronic converter focuses on small-scale, refined continuous compensation. Compared with the existing technology where the division of labor between the two types of regulation resources is unclear and continuous equipment is forced to replace discrete equipment for large-scale voltage regulation, this invention makes the regulation behavior of the power electronic converter more stable and centralized, and the actions of discrete equipment more phased and regular, thus improving the coordination and regulation quality of the voltage regulation system.

[0023] 4) This invention integrates various regulation resources, such as on-load tap changers, capacitor banks, power electronic converters, and photovoltaic inverters, into a unified discrete-continuous dual-layer collaborative optimization framework for joint operation, fully leveraging the complementary advantages of discrete coarse adjustment and continuous fine adjustment. Compared with existing technologies where various regulation methods are controlled locally and lack system-level coordination, this invention can effectively suppress the phenomenon of local voltage exceeding the upper limit at photovoltaic grid-connected nodes, raise the low voltage at the end of the feeder, reduce system voltage deviation, and improve node voltage distribution, thereby improving the voltage quality and photovoltaic absorption capacity of the distribution network in scenarios with high proportion of photovoltaic access.

[0024] 5) The synergistic optimization of this invention aims to suppress voltage overruns, reduce the number of on-load tap changer adjustments, lower capacitor bank switching costs, reduce network losses, and improve the smoothness of continuous regulation. While ensuring voltage compliance, it reduces the frequent operation of mechanical tap changers and capacitor banks. Compared to existing technologies that only target voltage deviation, this invention can extend the service life of on-load tap changers, reduce distribution network losses, and achieve a balance between voltage quality, equipment lifespan, and operational economy.

[0025] 6) This invention employs a double-layer nested encoding and fuzzy triple black hole solution mechanism. The outer layer encodes only discrete control variables, while the inner layer solves for continuous control variables. It balances global exploration and local fine-grained search through three types of black hole centers, fuzzy control mutation, and adaptive parameter updates. Compared to traditional single particle swarm optimization algorithms, this invention effectively avoids getting trapped in local optima in discrete-continuous coupling optimization, improving convergence stability and solution feasibility, thus making the generated collaborative voltage regulation scheme valuable for engineering applications. Attached Figure Description

[0026] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a schematic diagram of a single-phase topology for a flexible on-load tap-changing transformer.

[0027] Figure 2 This is a schematic diagram showing the evolution of the PV curve of a flexible on-load tap-changing transformer under different tap-changing methods.

[0028] Figure 3 This is a flowchart illustrating the overall process of the distribution network end-voltage over-limit mitigation method considering the static stability operating domain of flexible on-load tap-changing transformers, as described in this invention.

[0029] Figure 4 This is a flowchart of the fuzzy triple black hole algorithm used in this invention.

[0030] Figure 5 A schematic diagram of the topology of the improved IEEE 33-node power distribution system.

[0031] Figure 6This is a predicted curve showing the output of distributed photovoltaic power versus the load power.

[0032] Figure 7 The graph shows the change in the maximum voltage deviation of the system before and after voltage regulation under the collaborative optimization scenario considering the constraints of the static stable operating domain.

[0033] Figure 8 This is a comparison chart of the regulation of the power electronic converter under two scenarios: with and without static stable operating domain constraints.

[0034] Figure 9 This is a comparison chart of the smoothness of power electronic converter regulation under two scenarios: with and without static stable operating domain constraints.

[0035] Figure 10 This is a comparison diagram of the on-load tap changer operation strategies under two scenarios: with and without static stable operating domain constraints. Detailed Implementation

[0036] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0037] This paper proposes a method for mitigating voltage exceedance at the distribution network end within the static stable operating domain of a flexible on-load tap-changing transformer (OTCT). The overall concept is as follows: A steady-state equivalent model of the OTCT is established based on the collaborative voltage regulation mechanism of the OCT and the power electronic converter. A static stable operating domain model and an equivalent turns ratio model are established based on PV curve characteristics, tap position switching relationships, and the continuous compensation capability of the power electronic converter. Static stable operating domain constraints are embedded into the distribution network system-level variables based on the mapping relationship between local operating quantities and distribution network head-end operating quantities. A discrete-continuous two-layer collaborative optimization model is constructed using the OCT tap position, capacitor bank switching status, power electronic converter regulation, and reactive power output of the photovoltaic inverter as control variables. A distribution network voltage exceedance mitigation model considering the stable operating boundary is constructed by establishing power flow balance constraints, equipment operation constraints, and static stable operating domain constraints. The fuzzy triple black hole algorithm is used to solve the established two-layer optimization model. Finally, simulation verification is performed in the MATLAB environment using the MATPOWER software package. This method can effectively suppress node voltage overshoot in scenarios with high proportion of photovoltaic grid connection while ensuring that the operating point of the flexible on-load tap-changing transformer is within the static stable operating range, thereby improving the coordination, precision and operational safety of distribution network voltage regulation.

[0038] Example 1: like Figure 3 As shown, the distribution network end voltage over-limit mitigation method of this embodiment includes the following steps: S1: Steady-state operation mechanism analysis of flexible on-load tap-changing transformers: Flexible on-load tap-changing transformers combine the discrete coarse adjustment capability of traditional on-load tap changers with the continuous fine adjustment capability of power electronic converters. Their single-phase topology is as follows: Figure 1 As shown. Analyzing its steady-state operation mechanism, the relationship between the grid-side voltage and the load-side voltage is as follows: (1); (2); In the formula: This is the equivalent voltage of the upstream power supply referred to the secondary side; This is the secondary side voltage; , These are the equivalent active power and equivalent reactive power downstream of the output side of the flexible on-load tap-changing transformer, respectively. , , These are the sum of the equivalent impedances, equivalent resistances, and equivalent reactances of the line and the power electronic converter, respectively. For transformer turns ratio; , These are the equivalent resistance and equivalent reactance of the line, respectively. , These are the equivalent resistance and equivalent reactance of the power electronic converter, respectively. It is the imaginary unit.

[0039] Separating the real and imaginary parts of the above equation, we get: (3); In the formula: for and The phase difference between them. Squaring and adding the two equations above, using... eliminate , get about quartic equation: (4); The load power factor relationship is as follows: (5); In the formula: This refers to the phase angle between the load-side voltage and current. Let be the apparent power of the load. Substituting the load power factor relationship into the above fourth-order equation and solving, we obtain the PV relationship between the secondary voltage and active power: (6); (7); In the formula: To solve for intermediate variables; The equivalent active power is The corresponding secondary voltage. This PV relationship shows that, for a given downstream transmission power level, the voltage regulation capability of a flexible on-load tap-changing transformer has an upper limit. This characteristic is the physical basis for the subsequent characterization of the static stable operating domain.

[0040] S2: Construction of Static Stable Operating Domain Model and Equivalent Variation Model: The above model describes the basic voltage regulation principle of a flexible on-load tap-changing transformer, which is a static model. However, in actual distribution network operation, load levels and distributed generation output vary significantly over different time periods, therefore the impact of time variables on the location of the operating point needs to be considered. Let... Transform the PV relationship into a quadratic equation in one variable: (8); For the system to operate stably, the following criterion must be met: the existence of a real voltage solution. (9); Its physical meaning is: when When the above quadratic equation has no real solution, it means that there is no stable voltage operating point at this active power level, and the system experiences static voltage instability. The corresponding running point is the nose point of the PV curve, which determines the first... The active power limit corresponding to the lower nose point of each gear. .

[0041] Power electronic converters inject compensation voltage Changing the equivalent ratio is expressed as: (10); In the formula: The turns ratio of a power electronic converter, which is obtained by providing a compensation voltage equivalent, is not the actual mechanical turns ratio, but an additional equivalent turns ratio obtained by equivalent conversion on the secondary side, and does not change the magnitude of the overall mechanical turns ratio. It represents the difference in turns ratio between two adjacent on-load tap changer positions.

[0042] Fixed gear Stable operation slices under Defined as And it satisfies: (11); In the formula: This is the on-load tap changer position; , Given respectively The lower and upper boundaries of the stable operating voltage. The above adjustment range constraint limits the equivalent transformation ratio of continuous compensation to within half a range, which allows the continuous fine adjustment to be precisely connected with the discrete coarse adjustment range of adjacent ranges, avoiding over-level compensation.

[0043] When load changes cause voltage deviations exceeding the regulation range of the power electronic converter, it is necessary to adjust the tap changer to expand the voltage regulation range. The turns ratio model is as follows: (12); In the formula: The tap changer ratio is for the on-load tap changer. , These are its minimum and maximum gears, respectively.

[0044] This determines the switching conditions for the voltage regulation mode: when and At that time, continuous regulation is performed independently by the power electronic converter; when And the running point is close At the boundary, the on-load tap changer is triggered to switch from the tap position. Adjust to Subsequently, the power electronic converter re-enters a small-range adjustment. Combining discrete tap-changing and continuous compensation capabilities, the equivalent turns ratio of the flexible on-load tap-changing transformer is: (13); In the formula: This refers to the equivalent turns ratio of a flexible on-load tap-changing transformer. For example... Figure 2 As shown, as the operating point moves, the PV curve evolves under the alternating action of discrete gear adjustment and continuous compensation, and the stable operating slices of each gear are connected in sequence to form a complete static stable operating domain.

[0045] S3: Mapping between local operating quantities and distribution network head-end operating quantities: To facilitate the embedding of the aforementioned local static model into the distribution network time-series collaborative optimization model, a flexible on-load tap-changing transformer is installed between the upstream power source node 0 and the distribution network's first-end node 1: the output voltage in the local model... Voltage corresponding to system layer node 1 Downstream equivalent active power Equivalent reactive power These correspond to the active power flow sent downstream from the branches of node 0 to node 1 to the distribution network. and the trend of no effort Gear positions in the static model With equivalent variation The corresponding expansion is to time period variables. and ,in: This is used to number the scheduling period. Correspondingly, the statically stable operating domain constraints are expressed at the system level as: (14); In the formula: Gear position at time t The corresponding stable running slice.

[0046] S4: Construction of a multi-device collaborative voltage limit mitigation model: S4.1. Discrete layer modeling: The discrete layer provides the on-load tap changer position and capacitor bank switching status, which determines the system voltage reference level and discrete reactive power compensation capability.

[0047] Capacitor banks are mainly used for discrete reactive power compensation and regulating the voltage level of the distribution network. Their switching constraints are as follows: (15); In the formula: This represents the number of capacitor banks put into operation at node i at time t. This is the maximum number of groups that can be included. The reactive power provided by the capacitor bank at node i at time t; This is the rated capacity for a single group; The 0-1 variables characterizing the input state of the s-th group of capacitors are monotonically decreasing and constrained to avoid repeated counting of input combinations. , These are 0-1 variables representing the increase and decrease in the number of input groups, respectively. The mutual exclusion constraint between the two ensures that input and removal do not occur at the same time. This is the daily maximum number of switching operations allowed, used to limit the impact of frequent switching on equipment lifespan; This is the set of scheduling time periods.

[0048] The tap position constraints for on-load tap changers are: (16); In the formula: This is an indicator function, taking the value 1 if the condition is true and 0 otherwise; This represents the maximum number of tap changes allowed per day, used to limit the number of mechanical actions of the tap changer.

[0049] S4.2. Continuous Layer Modeling: The continuous layer corresponds to the continuous control variables in the system, including the equivalent turns ratio adjustment of the power electronic converter. Reactive power compensation Reactive power output of photovoltaic inverters .

[0050] Photovoltaic inverters are based on grid connection point voltage With voltage reference point , , , , Segmented operation based on relative position: When the grid connection point voltage is lower than When the voltage is at its maximum, the inverter compensates according to its maximum reactive power capacity; when the voltage is at its maximum, the inverter compensates according to its maximum reactive power capacity. and When the voltage is between [a certain value], reactive power control is performed according to the voltage deviation ratio; when the voltage is [a certain value]... and When the voltage is between, the inverter does not generate reactive power; when the voltage is between, the inverter does not generate reactive power. and When the voltage is between, reactive power is absorbed proportionally; when the voltage is between and Between these values, reactive power is absorbed at maximum capacity and active power output is reduced proportionally; when the voltage is higher than [a certain value], [the system] absorbs reactive power at maximum capacity and reduces active power output proportionally; At this time, the active power output drops to 0. Its active and reactive power outputs satisfy: (17); Its maximum available reactive power capacity is: (18); In the formula: Let be the maximum power point tracking active power of the photovoltaic system at node i at time t; This refers to the actual active power connected to the grid. This is reactive power output; This represents the maximum available reactive power capacity. This refers to the apparent power capacity of the photovoltaic inverter.

[0051] The voltage regulation model for power electronic converters is as follows: (19); In the formula: This is the maximum allowable change in the equivalent ratio adjustment between adjacent time periods, used to ensure the smoothness of continuous adjustment; Let be the current amplitude of the interface branch at time t. Its conjugate; The equivalent voltage of the upstream power supply referred to the secondary side at time t; , These are the equivalent active power component and reactive power component of the power electronic converter, respectively. Given its apparent power capacity, the last equation above is its capacity constraint. , These are operations for taking the imaginary part and the real part, respectively.

[0052] S5: Establishing the objective function and constraints: S5.1. Power Flow Balance Constraints and Static Stability Domain Constraints: The power flow state of the distribution network is jointly determined by the control variables of the discrete layer and the continuous layer. Therefore, both power flow balance constraints and static stability domain constraints are shared coupling constraints in the two-layer model. (20); (twenty one); (twenty two); (twenty three); In the formula: , Let be the active power and reactive power of branch ij at time t, respectively; For downstream node indexing; For the set of line nodes; , Let be the active power and reactive power of the load at node i at time t, respectively. , These represent the active power loss and reactive power loss of branch ij, respectively. , Let be the resistance and reactance of branch ij, respectively; Let be the voltage at node j at time t; Let be the current amplitude of branch ij at time t.

[0053] Fixed gear At that time, a flexible on-load tap-changing transformer corresponds to a stable operation slice. The upper-level discrete variables determine the stable operating slice number corresponding to the current time period, while the lower-level continuous variables continuously adjust the operating points within that slice. The stable operating domain constraints are uniformly written as... .

[0054] S5.2. Objective Function: The discrete layer aims to suppress node voltage overshoot, reduce the number of switching operations, and lower switching costs. (twenty four); (25); (26); (27); In the formula: , , The weights of each component in the discrete layer satisfy the following conditions: ; The voltage over-limit penalty is implemented in the form of the sum of squares of the deviations from the upper and lower limits, taking into account both types of over-limit risks. This is the cost of file retrieval; For the cost of cutting; , These are the lower and upper voltage limits for node i, respectively.

[0055] The continuous layer performs fine-tuning of the continuous voltage regulation equipment based on the given gear positions and switching states of the discrete layer: (28); (29); (30); (31); In the formula: , , For the weights of each component in the continuous layer, satisfying ; This refers to network losses. To continuously adjust the resource utilization rate, a normalized form is adopted to avoid the impact of differences in the capacity dimensions of different equipment; To improve the smoothness of continuous regulation, abrupt changes in reactive power regulation between adjacent time periods are penalized. Let t be the upper limit of the reactive power output of the power electronic converter at time t.

[0056] S6: Solution using the fuzzy triple black hole algorithm: like Figure 4 As shown, the fuzzy triple black hole algorithm is used to solve the above two-layer optimization model. This algorithm performs its functions according to the process of "outer layer encoding - inner layer solving - fitness evaluation - black hole update - fuzzy mutation", as follows: S6.1. Double-layer nested encoding: Because this model adopts a double-layer nested solution framework, the outer layer particle only encodes the discrete layer control variables. The continuous layer control variables do not participate in the direct encoding of the outer layer particle, but are solved separately by the inner layer optimizer after the outer layer particle is given. (32); (33); (34); In the formula: For the first q During the nth iteration m Discrete decision variable encoding vectors for each upper-level particle; For the first q During the nth iteration m OLTC timing vector of each particle; For the first q During the nth iteration mThe capacitor bank switching state matrix of each particle; This is a vectorization operation for expanding a matrix row by row; For the first q During the nth iteration m A particle at the node i ,time t The number of capacitor banks put into operation; For the first q During the nth iteration, the 1st m Each particle at time t The OLTC gear.

[0057] (35); (36); (37); (38); In the formula: For the first q During the nth iteration m The continuous layer position vectors of each lower-level particle, i.e., the set of continuous control variables; For the first q During the nth iteration m PEC equivalent ratio adjustment vector for each particle; For the first q During the nth iteration m Individual particles t The equivalent ratio adjustment of PEC at any given time; For the first q During the nth iteration m PEC reactive power compensation timing vector for each particle; For the first q During the nth iteration m Individual particles t PEC reactive power compensation amount at any time; For the first q During the nth iteration m A photovoltaic inverter reactive power output matrix with individual particles; For the first q During the nth iteration m Individual particles t The reactive power output of the photovoltaic inverter at any given moment; This is a vectorization operation for expanding a matrix row by row.

[0058] S6.2. Initialization and Repair: The initial position and initial velocity of the particles are randomly generated according to the upper and lower bounds of the variables. (39); (40); Rounding correction after updating discrete variables: (41); (42); Repairing continuous variable boundary truncation: (43); In the formula: Number the particles; Number the dimensions; denoted as the number of capacitor banks put into operation at node i and time t after repair for the m-th particle in the q-th iteration; , These are the upper and lower bounds of the d-th dimension variable, respectively; , These are the upper and lower bounds of the d-th dimension velocity, respectively; is a random number uniformly distributed in the interval $[0,1]$; This is the floor function. The repair operation ensures that the updated particles always remain within the feasible range of the decision variables.

[0059] S6.3. Inner Layer Solution and Synthesis Fitness: Given discrete layer particles in the outer layer The inner layer aims to minimize the objective function of the continuous layer to find the optimal values ​​of the continuous control variables. (44); In the formula: Given discrete-layer particle conditions, this represents the optimal solution for continuous-layer decision variables. The overall fitness is defined as: (45); In the formula: The weight coefficients for each item satisfy the following conditions: Each penalty item is used to convert the degree of constraint violation into fitness, and they are as follows: (46); (47); (47); (49); In the formula: This is a penalty item for voltage exceeding the limit; This is a penalty term for the statically stable operating domain, used to drive the operating point back to the stable operating slice. , Given time t The lower and upper voltage limits allowed in the lower static stable operating domain; As a penalty for mismatch with trends, , These are the active and reactive power flow balance residuals of node i at time t, respectively. This is a penalty item for exceeding the limit without performing any work; This refers to the set of nodes connected to the photovoltaic inverter.

[0060] S6.4. Triple Black Hole Update and Fuzzy Mutation: Setting Three Types of Black Hole Centers: (50); In the formula: Let be the globally optimal particle position in the q-th iteration; , These are the upper and lower bound vectors of the search space, respectively. The three black hole centers are respectively positioned at the global optimal position, the midpoint between the global optimal position and the upper bound, and the midpoint between the global optimal position and the lower bound. This guides particles to gather towards the optimal region while also exploring the upper and lower bound regions of the search space, preventing the population from prematurely gathering at a single point.

[0061] When the particle is outside the influence range of the black hole, the velocity-position formula is used for updating: (51); (52); In the formula: Inertial weight; , These are individual learning factors and group learning factors, respectively. , A random number in the interval [0,1]. The optimal position for an individual.

[0062] When a particle enters the black hole's influence zone, a confidence strategy is introduced to perform either capture update or escape update: (53); In the formula: The radius of influence of the black hole; Let be the confidence coefficient for the q-th iteration; , , A random number in the interval [0,1]; The maximum number of iterations is denoted by . The confidence strategy allows trapped particles to migrate to the global optimum with a high probability and escape to the upper and lower boundary center with a certain probability, thus achieving a balance between convergence and diversity.

[0063] To enhance population diversity, fuzzy control of mutation probability is defined: (54); And perform mutation updates on particles that meet the mutation conditions: (55); In the formula: This is the mapping function for the fuzzy controller, which uses the optimal fitness value of the current population. fitness standard deviation and fitness fluctuation value As input, when the fitness of the population tends to be concentrated, the mutation probability is increased to escape the local optimum; when the population is in an effective exploration state, the mutation probability is reduced to protect the superior individuals. Let be the variable-length coefficient of the d-th dimension variable; It is a random number in the interval [0,1].

[0064] Simultaneously, an adaptive parameter update strategy is introduced: (56); In the formula: , These are the upper and lower limits of the inertia weight, respectively; , and , These represent the upper and lower bounds of the individual learning factor and the group learning factor, respectively. The inertia weight decreases linearly with iteration, ensuring strong global search capability in the early stages and enhancing local convergence capability in the later stages. The learning factor increases quadratically with iteration, causing particles to converge to the optimal position more quickly in the later stages. After convergence, the cooperative voltage regulation scheme corresponding to the optimal particle is output.

[0065] S6.5. Evaluation Indicators for Boundary Control Effectiveness: To further verify the practical role of static stability operating domain constraints in multi-device collaborative voltage management, in addition to comparing the power electronic converter's regulation trajectory, tap-shifting action mode, and key node voltage response, the number of boundary triggers is defined. Minimum nose point margin and saturation duration ratio Three indicators are used for quantitative evaluation. The number of boundary triggers represents the equivalent adjustment. The number of times the adjustment boundary is reached and gear shifting is triggered; the minimum nose point margin represents the minimum power margin of the system operating point relative to the nose point limit of the current gear; the saturation duration ratio represents the proportion of time periods when the adjustment amount is close to its upper and lower boundaries out of the total number of time periods. (57); (58); In the formula: The gear corresponding to time t The PV curve nose point has the active power limit; $T$ is the threshold for determining proximity to the boundary; $|T|$ is the total number of scheduling periods.

[0066] S7: Application and Simulation Verification of Collaborative Voltage Regulation Scheme The collaborative voltage regulation scheme obtained from the S6 solution is applied to the operation and control of the distribution network to achieve voltage over-limit management at the end of the distribution network in scenarios with a high proportion of photovoltaic (PV) grid connection. Simulation verification is performed in the MATLAB environment using the MATPOWER software package. Specifically, the process includes: first, substituting the multi-device collaborative model into the fuzzy triple black hole algorithm and writing a calculation program; then, setting the simulation input conditions, including key parameters such as PV and load data, equipment parameters, algorithm parameters, and grid connection node locations; finally, running the calculation program by changing the input parameters, obtaining the corresponding result indicators, and comparing the results with and without static stable operating domain constraints under the same algorithm conditions to analyze the effectiveness of the proposed method in managing voltage over-limits.

[0067] Example 2: like Figure 5 As shown, a case study is conducted using an improved IEEE 33-node power distribution system, with a flexible on-load tap-changing transformer installed between the upstream power node and node 1. Figure 6 The predicted curves for load active power and photovoltaic active power output are shown in Table 1. The main parameters of the example are shown in Table 1, and the main parameter settings for the fuzzy triple black hole algorithm are shown in Table 2.

[0068]

[0069]

[0070] Three comparison scenarios are set up: Scenario 1 is a multi-device collaborative scheme without considering the constraints of the static stable operating domain; Scenario 2 is a multi-device collaborative scheme considering the constraints of the static stable operating domain, i.e., the scheme of this invention; Scenario 3 is the baseline scheme, which only performs power flow calculations on the improved IEEE 33-node system.

[0071] Figure 7 This is the curve showing the change in the maximum voltage deviation of the system before and after voltage regulation in Scenario 2. Figure 7 It can be seen that the maximum voltage deviation of the system after optimization in scenario 2 is suppressed in most periods, especially during the periods of high photovoltaic output at noon and significant load fluctuations in the evening. This shows that the collaborative optimization strategy considering the constraints of the static stable operating domain has advantages in mitigating extreme voltage fluctuations.

[0072]

[0073] As shown in Table 3, compared with the baseline scenario 3, the maximum node voltage in both scenario 1 and scenario 2 decreased from 1.052 pu to 1.000 pu, indicating that the collaborative optimization has a significant inhibitory effect on voltage exceeding the upper limit. The minimum node voltage increased to 0.579 pu and 0.610 pu, respectively, and the maximum voltage deviation decreased to 0.421 pu and 0.390 pu, respectively, indicating that both optimization scenarios can alleviate extreme voltage deviations. Among them, scenario 2, which considers the constraints of the static stable operating domain, performs better in raising the minimum voltage and reducing the maximum deviation.

[0074]

[0075] As shown in Table 4, after considering the static stable operating domain constraint, the overall system head-end operating point is far away from the stability boundary, the minimum nose point margin increases from 1.632 MW to 1.795 MW; the saturation duration ratio decreases from 4.17% to 0, and the number of boundary triggers decreases from 1 to 0. This indicates that the static stable operating domain constraint can effectively suppress the behavior of the power electronic converter approaching the regulation boundary in certain periods and improve the safety margin of the head-end operating point.

[0076] Figure 8 and Figure 9 The comparisons of the regulation magnitude and smoothness of the power electronic converter under two scenarios are presented. Compared to Scenario 1, the overall amplitude of the regulation trajectory in Scenario 2 is smaller, and the increments in adjacent time periods are more concentrated. This indicates that under the constraints of the static stable operating domain, the power electronic converter undertakes more small-scale, refined compensation tasks, rather than replacing discrete equipment for large-scale voltage regulation. The maximum value, standard deviation, and interquartile range of its regulation increment all decrease significantly, while the average value only decreases slightly. This suggests that the main effect of the static stable operating domain constraints is not to significantly reduce the average regulation level, but rather to reduce the violent fluctuations and dispersion near the boundary, making the regulation behavior more stable and concentrated.

[0077] Figure 10 This paper compares the on-load tap changer operation strategies under two scenarios. Considering the constraints of the static stability operating domain, the tap changer operation becomes more phased and regular. The system no longer relies solely on the power electronic converter to complete continuous corrections; instead, it uses the discrete tap changer capability to readjust the head-end voltage reference in a timely manner, thus preserving reasonable fine-tuning space for the power electronic converter at the overall level. Therefore, the practical effect of the static stability operating domain constraints is mainly reflected in: firstly, increasing the safety margin of the relative stability boundary of the operating point and suppressing saturation and boundary triggering; and secondly, strengthening the hierarchical coordination relationship from discrete coarse adjustment to continuous fine adjustment, making the functional division of the two types of regulation resources clearer.

Claims

1. A method for mitigating voltage exceedance at the end of a distribution network considering the static stability operating domain of a flexible on-load tap-changing transformer, characterized in that... Includes the following steps: S1: Analyze the steady-state operation mechanism of flexible on-load tap-changing transformers and establish the coordinated tap-changing relationship between discrete tap changer adjustment and continuous compensation of power electronic converter; S2: Based on the coordinated voltage regulation relationship of S1, construct the static stable operation domain model and equivalent turns ratio model of the flexible on-load tap-changing transformer, and obtain the stable operation slices under each on-load tap-changing switch position. S3: Map the static stable operating domain to the distribution network system layer variables and establish the correspondence between the local operating quantities of the flexible on-load tap-changing transformer and the operating quantities at the head end of the distribution network; S4: Based on the correspondence in S3, construct a multi-device collaborative voltage over-limit management model, taking the on-load tap changer position and capacitor bank switching status as discrete control variables, and the power electronic converter regulation and photovoltaic inverter reactive power output as continuous control variables, and determine the constraints of each control variable. S5: Based on the constraints in S4, establish the objective function and apply power flow balance constraints and static stability operating domain constraints to obtain the distribution network voltage over-limit management optimization model; S6: Solve the distribution network voltage over-limit management optimization model to obtain the coordinated voltage regulation scheme; S7: Apply the coordinated voltage regulation scheme to the operation control of the distribution network to achieve the management of voltage over-limit at the end of the distribution network.

2. The method for mitigating voltage exceedance at the end of a distribution network considering the static stability operating domain of a flexible on-load tap-changing transformer, as described in claim 1, is characterized in that: S1 includes: S1.1: Establish the voltage relationship between the primary and secondary sides of the flexible on-load tap-changing transformer: ； In the formula: This is the equivalent voltage of the upstream power supply referred to the secondary side; This is the secondary side voltage; , These are the equivalent active power and equivalent reactive power downstream of the output side of the flexible on-load tap-changing transformer, respectively. , These are the sum of the equivalent resistances and the sum of the equivalent reactances of the line and the power electronic converter, respectively. The imaginary unit; S1.2: Separate the real and imaginary parts of the voltage relationship in S1.1, and eliminate the phase difference by squaring. Later, we obtained information about The fourth equation, and then the load power factor relationship Substituting the values ​​into the equation, we obtain the PV relationship between the secondary voltage and active power: ； In the formula: for and The phase difference between them; This refers to the phase angle between the load-side voltage and current. This is the sum of the equivalent impedances of the line and the power electronic converter; To solve for intermediate variables; The equivalent active power is The corresponding secondary voltage at that time.

3. The method for mitigating voltage exceedance at the end of a distribution network considering the static stability operating domain of a flexible on-load tap-changing transformer, as described in claim 2, is characterized in that: S2 includes: S2.1: Based on the PV relation obtained in S1.2, let... Transform it into a quadratic equation in one variable: ； Where: is the criterion for the existence of a stable voltage solution in the system. Determine the active power limit corresponding to the nose point of the PV curve; To replace the variable, ; The coefficient of the linear term; For constant terms; For transformer turns ratio; S2.2: Within the active power limit range determined in S2.1, establish the equivalent turns ratio of the power electronic converter. and its adjustment range Based on this, a stable operation slice under a fixed on-load tap changer position is constructed. ,Right now And it satisfies: ； ； ； In the formula: Compensation voltage injected into the power electronic converter; This is the difference in turns ratio between two adjacent on-load tap changer positions. This is the position of the on-load tap changer; For the first The active power limit corresponding to the nose point of the PV curve at each gear level; For gear position number; , Given respectively The lower and upper boundaries of the stable operating voltage; S2.3: Determine the voltage regulation mode switching conditions based on the stable operation slice constructed in S2.2: when and At that time, continuous adjustment is performed by the power electronic converter; when And the running point is close At the boundary, the on-load tap changer is triggered to switch from the tap position. Adjust to Subsequently, the power electronic converter re-entered a small-range regulation; and an equivalent turns ratio model for the flexible on-load tap-changing transformer was established: ； In the formula: This is the equivalent turns ratio of a flexible on-load tap-changing transformer.

4. The method for mitigating voltage exceedance at the end of a distribution network considering the static stability operating domain of a flexible on-load tap-changing transformer, as described in claim 3, is characterized in that: S3 includes: S3.1: Install a flexible on-load tap-changing transformer between upstream power supply node 0 and distribution network head-end node 1 to convert the output voltage in the local model. This corresponds to the voltage of system layer node 1. , Number the scheduling period; S3.2: Based on the voltage correspondence established in S3.1, the equivalent active power in the local model is... Equivalent reactive power These correspond to the active power flow sent downstream from the branch of node 0 to node 1 to the distribution network. and the trend of no effort ; S3.3: Based on the variable correspondence established in S3.1 and S3.2, adjust the on-load tap changer positions in the static model. Equivalent turns ratio of power electronic converter Expanded to time period variables and This makes the statically stable operating domain constraints express as: ； In the formula: Gear position at time t The corresponding stable running slice.

5. The method for mitigating voltage exceedance at the end of a distribution network considering the static stability operating domain of a flexible on-load tap-changing transformer, as described in claim 4, is characterized in that: In S4, the constraints on the discrete control variables include: S4.1: Establish capacitor bank switching constraints: ； ； ； In the formula: The node at time t i The number of capacitor banks put into operation; This is the maximum number of capacitor banks that can be connected. The node at time t i The reactive power provided by the capacitor bank; This refers to the rated capacity of a single capacitor bank. , These are 0-1 variables representing the increase or decrease in the number of capacitor banks being put into operation; This is the maximum number of times a capacitor bank can be switched on and off per day. For the set of scheduling periods; Number the nodes; S4.2: Based on the discrete reactive power compensation capability determined in S4.1, establish on-load tap changer position constraints: ； ； In the formula: , These are the minimum and maximum positions of the on-load tap changer, respectively. This is an indicator function, taking the value 1 if the condition is true and 0 otherwise; This represents the maximum number of file transfers allowed per day.

6. The method for mitigating voltage exceedance at the end of a distribution network considering the static stability operating domain of a flexible on-load tap-changing transformer, as described in claim 5, is characterized in that: In S4, the constraints on the continuous control variables include: S4.3: Establish reactive power output constraints for photovoltaic inverters: based on the photovoltaic grid connection point voltage. With voltage reference point , , , , The reactive power output of the photovoltaic inverter is determined by segmenting the relative positions. And its maximum available reactive power capacity is: ； In the formula: The apparent power capacity of the photovoltaic inverter; Let be the photovoltaic active power output of node i at time t; , , , , These are the five voltage reference points for the segmented control of the photovoltaic inverter; S4.4: Within the reactive power regulation capability boundary determined in S4.3, establish a voltage regulation model for the power electronic converter: ； In the formula: for t Equivalent transformation ratio at time; for t The equivalent turns ratio adjustment of the power electronic converter at any time; This represents the maximum permissible change in the equivalent ratio adjustment between adjacent time periods; , They are respectively t The active and reactive power delivered downstream by the interface branch of the flexible on-load tap-changing transformer at all times; for t Voltage at the beginning node of the distribution network at all times; for t The current amplitude of the interface branch at that time. Its conjugate; for t The equivalent voltage of the upstream power supply is calculated to the secondary side at all times; , These are the equivalent active power component and reactive power component of the power electronic converter, respectively. The apparent power capacity of the power electronic converter; , These are operations for taking the imaginary part and the real part, respectively.

7. The method for managing voltage exceedance at the end of a distribution network considering the static stability operating domain of a flexible on-load tap-changing transformer as described in claim 6, characterized in that: S5 includes: S5.1: Establish power flow balance constraints: ； In the formula: , Branch roads ij Active and reactive power; For downstream node indexing; For the set of line nodes; , These are the active and reactive power of the load, respectively. , These represent the active and reactive power losses of the branch circuit, respectively. , These are the branch resistance and reactance, respectively. Number the nodes; Let the voltage at node j be _____. This refers to the amplitude of the branch current. S5.2: Based on the power flow balance constraints established in S5.1, the static stable operating domain constraints are embedded as shared coupling constraints between discrete and continuous control variables: ； S5.3: Establish the objective function under the constraints of S5.1 and S5.2: ； ； ； ； In the above formula: The objective function is for the discrete layer. For continuous layer objective function; This is a penalty item for voltage exceeding the limit; This is the cost of transferring the file; For the cost of cutting; , These are the lower and upper voltage limits for node i, respectively; , , The weights of each component in the discrete layer; This refers to network losses. This is a continuously adjusting resource utilization rate item; To adjust the smoothness term; , , These represent the weights of each component in the continuous layer.

8. The method for managing voltage exceedance at the end of a distribution network considering the static stability operating domain of a flexible on-load tap-changing transformer as described in claim 7, characterized in that: The S6 algorithm employs a fuzzy triple black hole algorithm for solution, including: S6.1: Employs double-layer nested encoding: Outer particles only encode discrete control variables ; Continuous control variables It does not participate in the outer layer encoding and is solved independently by the inner layer after the outer layer particles are given. In the formula: This is the gear timing vector; This is the switching state matrix for the capacitor bank; This is the equivalent variable ratio adjustment vector; This is the reactive power compensation timing vector; This is the reactive power output matrix for a photovoltaic inverter. This is a vectorization operation performed by expanding by row; , These are the particle number and the number of iterations, respectively. , These are the discrete layer and continuous layer encoding vectors, respectively. S6.2: Randomly generate initial positions for particles encoded in S6.1 according to the upper and lower bounds of the variables: Based on the initial velocity, and to repair the updated particles: Discrete variables by Rounding and repair, continuous variables according to Boundary truncation repair; In the formula: Number the particles; Number the dimensions; This represents the number of iterations. , These are the upper and lower bounds of the d-th dimension variable, respectively; is a random number uniformly distributed in the interval [0,1]. It is a rounding function; S6.3: For each outer layer particle after S6.2 repair, the inner layer aims to minimize the continuous layer objective function, solve for the optimal value of the continuous control variable, and then use the discrete layer objective function value, the continuous layer objective function value and the constraint violation penalty term as weights to form the comprehensive fitness; S6.4: Based on the comprehensive fitness obtained in S6.3, update the individual optimal position and the global optimal position, use the triple black hole mechanism to update the particle position, and perform mutation on the particle with the mutation probability determined by fuzzy control. After iterating to convergence, output the cooperative voltage regulation scheme.

9. The method for mitigating voltage exceedance at the end of a distribution network considering the static stability operating domain of a flexible on-load tap-changing transformer, as described in claim 8, is characterized in that: In S6.3, the overall fitness is: ； ； In the formula: , These are the objective function values ​​for the discrete layer and the continuous layer, respectively. These are the weighting coefficients for each item; ； ； ； ； In the formula: This is a penalty item for voltage exceeding the limit; For statically stable operating domain penalty items, , Given time t The lower and upper voltage limits allowed in the lower static stable operating domain; As a penalty for mismatch with trends, , These are the active power flow balance residuals and reactive power flow balance residuals of node i at time t, respectively. This is a penalty item for exceeding the limit without performing any work. Let t be the upper limit of the reactive power output of the power electronic converter. This refers to the set of nodes connected to the photovoltaic inverter.

10. The method for managing voltage exceedance at the end of a distribution network considering the static stability operating domain of a flexible on-load tap-changing transformer as described in claim 9, characterized in that: S6.4 includes: S6.4.1: Setting the center of three types of black holes: ； In the formula: Let be the globally optimal particle position in the q-th iteration; , These are the upper and lower bound vectors of the search space, respectively; S6.4.2: Based on the black hole center setting in S6.4.1, when the particle is outside the black hole's influence range, update the particle velocity and position using the following formula: ； When a particle enters the black hole's influence range, a capture update or escape update is performed according to the confidence strategy. In the formula: Inertial weight; , These are individual learning factors and group learning factors, respectively. , A random number in the interval [0,1]; The optimal position for the individual; S6.4.3: Based on the position update in S6.4.2, adjust the mutation probability according to fuzzy control. Perform mutation updates on particles that meet the mutation conditions: ； And adaptively update the inertia weights and learning factors according to the following formula: ； In the formula: For fuzzy controller mapping functions; , , These are the current population's optimal fitness value, fitness standard deviation, and fitness fluctuation value, respectively. Let be the variable-length coefficient of the d-th dimension variable; A random number in the interval [0,1]; , These are the upper and lower limits of the inertia weight, respectively; , These are the upper and lower limits of the individual learning factor, respectively; , These are the upper and lower limits of the group learning factor, respectively. This represents the maximum number of iterations.

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