Power distribution network correction control method, system and device considering thermal characteristics of three-core cable

Abstract

The present application relates to a kind of distribution network correction control method, system and equipment considering the thermal characteristics of three-core cable, belong to electric power system engineering field, comprising: obtaining active distribution network operation data and three-core cable physical structure parameters, based on initial power flow calculation fault time branch cable initial steady-state temperature of each layer;Three-node equivalent transient thermal circuit model of three-core cable is constructed, and linearization processing is carried out to electric-thermal nonlinear term in combination with two-stage boundary dynamic shrinkage strategy;The discretized cable transient temperature rise state equation is embedded as safety check constraint in fault reconstruction dynamic optimization model and solved.The present application replaces the traditional static current limit constraint by real-time prediction of cable transient temperature rise trajectory after fault reconstruction, fully taps the thermal inertia potential and transient overload capacity of cable, ensures the physical thermal safety of reconstruction scheme under emergency working condition, significantly improves the load recovery rate and distributed photovoltaic accommodation capacity of active distribution network.

Description

Technical Field

[0001] This invention relates to a power distribution network correction and control method, system, and equipment that takes into account the thermal characteristics of a three-core cable, belonging to the field of power system engineering technology. Background Technology

[0002] With the increasing penetration of distributed generation in Active Distribution Networks (ADNs), fault reconfiguration, as a key technology for enhancing the self-healing capability and power supply reliability of distribution networks, is becoming increasingly important. Fault reconfiguration changes the network topology by optimizing and adjusting the states of tie switches and sectionalizing switches to achieve load transfer after a fault and effective absorption of distributed generation. Given the complex and ever-changing operating conditions of distribution networks, real-time monitoring and safety correction of line equipment operating status are crucial for ensuring that the entire fault reconfiguration process meets various electrical safety constraints and maintains stable system operation.

[0003] Currently, in the field of active distribution network fault reconfiguration and safety assessment, existing research has made some progress in algorithm optimization and physical modeling. At the algorithmic level, for distribution network topology optimization problems, some researchers have proposed fault recovery schemes based on heuristic search or mathematical programming. Through methods such as second-order cone programming or mixed-integer linear programming, they aim to maximize load transfer while satisfying electrical constraints such as voltage and current. Building upon this, considering the power fluctuations caused by distributed generation, some scholars have further introduced stochastic scenario generation or robust optimization theory to improve the adaptability of reconfiguration schemes under uncertain environments. At the physical modeling level, with the development of Electro-Thermal Coordination (ETC) theory, the thermal safety assessment of equipment is receiving increasing attention. For example, for overhead conductors, Dynamic Thermal Rating (DTR) technology has been widely studied. It establishes a steady-state thermal balance equation by combining real-time environmental meteorological parameters, using the real-time conductor temperature rather than the static current limit as the operating boundary. For underground cables, which are more relevant to this invention, existing research has analyzed the transient response of the cable core temperature to the load current by constructing an equivalent thermal circuit model, laying a theoretical foundation for accurately assessing its transmission potential.

[0004] However, simply superimposing the aforementioned network topology optimization algorithm with the cable transient thermal model for real-time fault reconstruction still presents some unresolved problems. Existing safety verification logic generally ignores the dynamic thermal inertia of three-core underground cables and their buried environment, leading to a disconnect between the reconstruction decision logic and the actual physical evolution process. On the one hand, most existing reconstruction models still use the traditional static thermal rating (STR) as a rigid current limit, ignoring the significant hysteresis characteristic of the cable core temperature response to current surges. This results in the cable's inherent "transient thermal overload window" being ignored during the emergency period after fault transfer, and the conservative verification logic based on the static rated current carrying capacity often leads to some safe and feasible transfer schemes being misjudged as infeasible or unsafe, resulting in unnecessary load shedding. More critically, due to the nonlinear term of the electro-thermal term in the cable temperature rise equation being coupled with the discrete switching variables in topology reconstruction, the model evolves into a difficult-to-solve non-convex mixed-integer non-linear programming (MINLP) problem. Existing methods cannot guarantee the mathematical convergence of such complex coupled models, making it difficult to effectively integrate physical temperature rise constraints with discrete reconstruction algorithms. Therefore, breaking down the mathematical barrier between nonlinear thermal constraints and topological variables, and achieving physical compatibility and model solvability of transient thermal boundaries in reconstruction decisions, is a technical bottleneck that urgently needs to be overcome in this field. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a power distribution network correction and control method, system, and device that takes into account the thermal characteristics of three-core cables. The aim is to establish physical constraints that accurately characterize the transient thermal dynamic process of cables, using the core temperature of the cable as the essential indicator for determining the transmission boundary of branches, replacing the traditional static current limit constraints. This allows for the full exploitation of the overload potential of cables while ensuring the safe operation of the power distribution network, thereby optimizing fault reconfiguration schemes and ensuring safe correction, and improving the power supply guarantee capability and fault recovery economy of the power distribution network under extreme conditions.

[0006] This invention starts from the physical essence of cable thermal safety, establishes a transient temperature rise model that can characterize the thermal dynamic process of a three-core cable, and embeds it as a core safety constraint into the fault reconstruction dynamic optimization framework. The real-time conductor temperature replaces the traditional static current limit as the safety criterion, thereby achieving a deep integration of reconstruction decision-making and thermal safety verification.

[0007] The technical solution of the present invention is as follows:

[0008] A power distribution network correction and control method considering the thermal characteristics of a three-core cable includes the following steps:

[0009] S1, Basic data acquisition and initial steady-state temperature calculation at the time of failure:

[0010] Acquire basic operational data of the active distribution network (including distribution network topology parameters, load time sequence data, distributed photovoltaic power output data, etc.), radial physical structural parameters of the three-core cable (including outer diameter of each layer and conductor cross-sectional area), and thermal parameters (thermal resistivity and volumetric heat capacity of each layer of cable dielectric material, thermal resistivity and volumetric heat capacity of the surrounding soil, cable burial depth, and ambient temperature, etc.); based on the initial power flow distribution before the fault occurs, combined with the steady-state thermal balance equations of the three-core cable, calculate the initial steady-state temperature of the conductor, inner lining, and armor layer of each branch cable at the preset fault occurrence time.

[0011] S2, Dynamic thermal circuit model construction, discretization, and linearization:

[0012] A three-node equivalent transient thermal circuit model capable of characterizing the dynamic temperature changes of each layer of the cable is established. The differential equation of the equivalent transient thermal circuit is discretized to obtain the transient temperature rise state equation reflecting the relationship between the temperature at the next moment and the temperature at the current moment. The McCormick envelope method is used to linearize the electro-thermal nonlinear coupling terms in the transient temperature rise state equation, transforming them into a set of linear inequality constraints, and a two-stage boundary dynamic contraction strategy is used for solving the problem.

[0013] S3, Construction and solution of dynamic optimization model for fault reconstruction:

[0014] A fault reconfiguration dynamic optimization model is constructed with the objective function of minimizing the overall system operating cost. The linearized transient temperature rise state equation is embedded into the fault reconfiguration dynamic optimization model as a thermal safety verification constraint. By limiting the maximum temperature of the cable conductor within the reconfiguration look-ahead time window to not exceed the maximum allowable temperature, the fault reconfiguration dynamic optimization model is solved in combination with the distribution network electrical constraints. The optimal fault reconfiguration topology scheme considering the thermal inertia safety boundary of the three-core cable is obtained, along with the corresponding load shedding, distributed photovoltaic curtailment, branch current, and temperature trajectory data.

[0015] Preferably, in step S1, the steady-state thermal balance equations for the three-core cable are:

[0016] (4)

[0017] In the formula, The initial current of the branch before the fault occurred has a nominal value; This refers to the number of cable cores. , , , respectively, are the initial steady-state temperatures of the cable conductor, inner lining, and armor layer at the moment the fault occurs, in °C; The ambient temperature; AC resistance of conductors taking into account temperature effects; This refers to the loss of the three-phase insulating dielectric. , These are the sheath loss coefficient and the armor loss coefficient, respectively. to These are the equivalent thermal resistances of the insulation layer, inner lining layer, armor layer, and soil layer, respectively.

[0018] Preferably, in step S2, the equivalent transient thermal circuit model is expressed as:

[0019] (5)

[0020] In the formula, , , The temperatures of the conductor layer, inner liner layer, and armor layer at time t are respectively, in °C; The conductor Joule loss over time t; , , These are the effective heat capacities of conductor nodes, inner liner nodes, armor layers, and the external environment of the cable, respectively.

[0021] The differential equations of the equivalent transient thermal circuit model are discretized using the implicit trapezoidal rule to obtain the transient temperature rise state equation:

[0022] (6)

[0023] In the formula, the subscript Indicates the first The values ​​at each time segment; Let s be the difference step size. , , , respectively, are the temperatures of the conductor layer, inner liner layer, and armor layer at the t-th time segment, in °C; Let be the conductor loss at the t-th time segment; , These are the effective heat capacities of the conductor node and the inner liner node, respectively, after correction by the Van Wormer coefficient. This is the equivalent heat capacity of the armor layer and the external environment of the cable.

[0024] Preferably, the effective heat capacity of each node is obtained by distributing and summing the heat capacity of each layer of the cable and part of the soil, the process of which is as follows:

[0025] First, calculate the volumetric heat capacity of each physical layer of the cable:

[0026] (7)

[0027] (8)

[0028] (9)

[0029] (10)

[0030] (11)

[0031] (12)

[0032] In the formula, , , , , , These are the heat capacities of the conductor, insulation layer, inner lining layer, armor layer, outer sheath, and effective soil layer, respectively. , , , , , These are the unit volume heat capacities of the conductor, insulation layer, inner lining layer, armor layer, outer sheath, and effective soil layer, respectively. The cross-sectional area of ​​the conductor; The diameter of the conductor; , , , These are respectively the insulation layer, inner lining layer, armor layer, and total outer diameter of the cable; The effective soil diameter, physically representing a characteristic diameter reflecting the extent of heat diffusion, is numerically determined based on a preset reconstruction look-ahead time window. And the thermal diffusion characteristics of the soil are determined, specifically satisfying:

[0033] (13)

[0034] In the formula, This is a preset reference period (e.g., 24 hours). This is the reference characteristic diameter determined based on the soil thermal diffusion characteristics under this reference period (e.g., a typical value of 211 mm). The current reconstruction lookahead time window length;

[0035] To accurately simulate the temperature gradient and thermal storage characteristics inside the insulation layer, the Van Wormer coefficient was used. The thermal capacity of the insulating layer is distributed to adjacent thermal nodes, calculated using the following formula:

[0036] (14)

[0037] To effectively map the heat capacity of each physical layer into the three-node equivalent transient thermal path model, the Van Wormer coefficient allocation method is used to recombine the heat capacity, and the effective heat capacity of the conductor node, the inner liner node, and the armor layer node is calculated. , , The specific formula is as follows:

[0038] (15)

[0039] (16)

[0040] (17)

[0041] In the formula, The effective heat capacity of the conductor node, The effective heat capacity of the inner lining node, The effective heat capacity of the armor node;

[0042] Preferred, to The formulas for calculating the equivalent thermal resistance of the insulation layer, inner lining layer, armor layer, and soil layer are as follows:

[0043] (18)

[0044] (19)

[0045] (20)

[0046] (twenty one)

[0047] In the formula, , , , These are respectively the insulation, inner lining, armor layer, and soil thermal resistivity; The depth is the cable burial depth. It should be noted that the soil thermal resistance given in formula (21) is... This describes the thermal boundary resistance of the cable throughout its entire path in an underground environment. Considering the conservative requirements of power distribution network safety correction, this invention uses this steady-state thermal resistance as the thermal boundary during the transient process to ensure that the estimate of cable temperature rise within the reconstruction look-ahead time window is always within the safe envelope.

[0048] Preferably, the McCormick envelope method is used to address the nonlinear coupling term between the square of the current and temperature in the transient temperature rise equation of state due to conductor Joule losses. Linearization is performed, specifically as follows:

[0049] Define nonlinear auxiliary variables The following set of linear inequalities are used to replace the non-convex product terms involving conductor losses in the transient temperature rise equation of state:

[0050] (twenty two)

[0051] In the formula, branch road At time step The per-unit value of the square of the current; and These are the maximum and minimum allowable values ​​for the conductor temperature, respectively. and These are the squares of the maximum and minimum currents of the branch, respectively; the transient temperature rise state equation is transformed into a linear constraint of the Mixed-Integer Quadratically Constrained Programming (MIQCP) model through linearization. and branch road The dynamic search boundary at different optimization stages, where Keep it at 0 to preserve the switching operation space for topology reconfiguration. A two-stage strategy is then used for dynamic contraction to reduce the relaxation error of the McCormick envelope.

[0052] Preferably, the solution process using a two-stage boundary dynamic shrinkage strategy is as follows:

[0053] (1) Coarse optimization stage: Set the square of the current in each branch. The initial search limit is the global maximum allowable value. The first round of optimization is performed to obtain the preliminary observation value of the square of the branch current.

[0054] (2) Fine optimization stage: Extract the maximum square value of the current in each branch observed in the first round, and then use the results from the second round of optimization. The search space is updated to the larger of a preset multiple of the observed maximum value and a preset safety lower limit, thereby constructing a more compact McCormick convex hull search space; the linear inequality set is regenerated based on the updated compact boundary and a second round of solving is performed to reduce linearization error.

[0055] Preferably, in step S3, the objective function of the fault reconfiguration dynamic optimization model is to minimize the overall operating cost of the distribution network within the reconfiguration look-ahead time window, as expressed below:

[0056] (twenty three)

[0057] In the formula, To reconstruct the total operating cost of the system within the look-ahead time window; For the total set of time steps, The unit time step; , , and These are the unit price of electricity purchased from the distribution network to the upper-level power grid, the unit cost of load shedding compensation, the unit cost of distributed photovoltaic curtailment penalty (yuan / MW·h), and the cost of a single operation of the tie switch (yuan / time), and the values ​​are taken in accordance with the principle that ensuring power supply security takes precedence over operational economy; For the first The total active power (MW) injected into the distribution network substation (balance node) at each time step; and They are nodes At time step Active load shedding and nodes At time step Distributed photovoltaic curtailment (MW). branch road At time step The switch action variable is a binary variable. If the first... Step switch state compared If a step switch occurs, set the value to 1; otherwise, set the value to 0.

[0058] Preferably, the electrical constraints of the distribution network are expressed using a branch power flow model based on the Big M method and second-order cone relaxation to ensure the electrical and topological safety and feasibility of the reconfiguration scheme. The specific formula is as follows:

[0059] (1) Node power balance constraints:

[0060] (twenty four)

[0061] (2) Branch voltage drop and switching logic coupling constraints:

[0062] (25)

[0063] (3) Second-Order Cone Programming (SOCP) Constraints:

[0064] (26)

[0065] (4) Radial constraints in network topology:

[0066] (27)

[0067] (5) Switching operation limits and voltage safety constraints:

[0068] (28)

[0069] (29)

[0070] In the formula, For time step; Number the nodes; and All are branch road numbers; It is the set of all branches in the system; To study the set of all time steps within a given time period; For inflow node The set of branch paths; outflow node The set of branch paths; and Branch roads The first and last nodes; and They are the branch roads that flow through. Active and reactive power, and They are time steps Flowing through the branch road The active and reactive power together constitute the node. Power inflow and outflow terms; and Branch roads Resistance and reactance; branch road At time step The magnitude of the current; , , They are nodes , , At time step The square of the voltage amplitude; and They are nodes At time step The predicted values ​​of active and reactive loads; and They are nodes At time step The active and reactive load shedding quantities; For nodes At time step The upper limit of the predicted active power output of distributed photovoltaic power generation. Adjust its reactive power output; For nodes At time step Distributed photovoltaic curtailment; For sufficiently large positive numbers; The number of nodes; This represents the maximum total number of actions allowed globally in the active distribution network. branch road The maximum number of handovers allowed during the refactoring cycle; and Branch roads exist Time and The binary switch state variable at any given time; and These are the upper and lower limits of the allowable node voltage amplitude, respectively;

[0071] To ensure the physical feasibility of distributed photovoltaic (PV) systems participating in voltage optimization support, active distribution network operation constraints also include apparent capacity limitations for distributed PV inverters:

[0072] (30)

[0073] In the formula, For nodes At time step The upper limit of the predicted active power output of distributed photovoltaic power; For nodes At time step Distributed photovoltaic curtailment; For distributed photovoltaic inverters in time step The amount of reactive power output adjustment provided; For installation on the node The rated apparent capacity of the distributed photovoltaic inverter at the location;

[0074] The physical boundary constraints of the cable, taking thermal inertia into account, are described as follows:

[0075] (31)

[0076] In the formula, The branch obtained in real time through the transient temperature rise state equation of the cable At time step The conductor core temperature, This refers to the rated permissible temperature of the cable insulation material. This constraint replaces the rigid constraint on the static current carrying capacity rating in traditional reconfiguration, allowing the transient current of the branch to exceed the steady-state limit after reconfiguration, provided that the conductor temperature does not exceed the rated limit of the insulation material. As the ultimate physical boundary for security.

[0077] A power distribution network correction control system that takes into account the thermal characteristics of a three-core cable, for implementing the above method, includes:

[0078] The basic data and structural parameter acquisition module is configured to acquire the basic operating data of the active distribution network to be corrected and the radial physical structural parameters of the three-core cable, and input the reconstruction look-ahead simulation time window and preset fault scenarios.

[0079] The initial steady-state temperature distribution calculation module is configured to calculate the initial steady-state temperature of the conductor, inner lining and armor layer of each branch cable at the preset fault occurrence time, based on the initial steady-state power flow distribution of the active distribution network and combined with the steady-state thermal balance equations of the three-core cable.

[0080] The transient temperature rise prediction and optimization modeling module is configured to establish a three-node equivalent transient thermal circuit model of a three-core cable, and embed the discretized transient temperature rise state equation of the cable as a constraint into the dynamic optimization model of active distribution network fault reconfiguration. At the same time, the electro-thermal nonlinear coupling terms in the state equation are linearized by the McCormick envelope method, and the linearized search space is updated and optimized by a two-stage boundary dynamic shrinkage strategy.

[0081] The optimal reconfiguration scheme output module is configured to solve the dynamic optimization model of fault reconfiguration. Based on satisfying the electrical and topological constraints of the distribution network, it takes the maximum temperature of the cable conductor within the reconfiguration time window not exceeding the rated temperature limit of the insulation material as the safety physical boundary and outputs the optimal fault reconfiguration topology scheme.

[0082] An electronic device is characterized by comprising a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the method described above.

[0083] The beneficial effects of this invention are as follows:

[0084] This invention constructs a discretized three-node transient thermal circuit model and uses the McCormick envelope method to linearize its nonlinear coupling terms, successfully transforming the complex electro-thermal coupling nonlinear constraints, which were originally difficult to solve directly, into an easily solvable mixed-integer quadratic constraint programming (MIQCP) problem. This technological breakthrough mathematically solves the problem of solving models containing discrete switching variables, laying the algorithmic foundation for the application of cable dynamic thermal characteristics in real-time optimization decision-making in power distribution networks.

[0085] In the safety verification of power distribution network operation, traditional reconfiguration strategies generally use the static thermal rating (STR) as a rigid current limit, ignoring the significant thermal inertia of three-core cables. This invention starts from the physical boundary of cable thermal safety, using a transient temperature rise state equation to replace the traditional current limit. This accurately characterizes the "current step - temperature rise lag" phenomenon generated at the moment of fault reconfiguration, thus fully utilizing the "transient thermal overload window" of the cable during fault reconfiguration. This makes the safety assessment results more consistent with actual operating conditions and effectively solves the problem of misjudgment of reconfiguration schemes caused by the overly conservative traditional verification logic.

[0086] By integrating the dynamic temperature rise trajectory of cables with the reconfiguration optimization model, this invention can maximize the transmission potential of active distribution network branches. In the event of a fault, this invention can significantly reduce unnecessary load shedding, improving the power supply recovery level and self-healing resilience of the distribution network. In renewable energy integration scenarios, this invention can effectively alleviate the problem of curtailment caused by short-term line overload, significantly improving the system's ability to absorb renewable energy, and achieving a balance between the operational safety and efficiency of the distribution network. Attached Figure Description

[0087] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an undue limitation of this application.

[0088] Figure 1 This is a flowchart of the power distribution network correction and control method that takes into account the thermal characteristics of a three-core cable according to the present invention.

[0089] Figure 2 This is a flowchart of the active distribution network fault reconfiguration dynamic optimization solution algorithm of a certain embodiment of the present invention;

[0090] Figure 3 This is a schematic diagram of the equivalent transient thermal path model of a three-core cable at three nodes and its heat flow direction according to a certain embodiment of the present invention;

[0091] Figure 4 A schematic diagram of a 33-node active distribution network reference topology and fault location provided in a certain embodiment of the present invention;

[0092] Figure 5 A comparison diagram of transient current and temperature response of key branches after fault reconstruction under the strategy of the present invention and the control scheme in a scenario (evening peak heavy load) provided by a certain embodiment of the present invention;

[0093] Figure 6 A comparison chart of load shedding amounts between the method of the present invention and a control scheme under a scenario (heavy load during evening peak hours) provided in a certain embodiment of the present invention;

[0094] Figure 7This is a snapshot of the node voltage and branch thermal load rate distribution at critical moments in the scenario (evening peak heavy load) provided by the embodiments of the present invention. Detailed Implementation

[0095] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. However, this is not the only description; all aspects not described in detail herein are based on conventional techniques in the art.

[0096] Example 1

[0097] A power distribution network correction and control method that takes into account the thermal characteristics of three-core cables, such as Figure 1 As shown, it includes the following steps:

[0098] S1, Basic data acquisition and initial steady-state temperature calculation at the time of failure:

[0099] Acquire basic operational data of the active distribution network (including distribution network topology parameters, load time series data, distributed photovoltaic power output data, etc.), radial physical structure parameters of the three-core cable (including outer diameter of each layer and conductor cross-sectional area), and thermal parameters (thermal resistivity and volumetric heat capacity of each layer of cable dielectric material, thermal resistivity and volumetric heat capacity of the surrounding soil, cable burial depth, and ambient temperature, etc.). Input the reconstruction look-ahead time window, preset fault scenarios, and initial distribution network topology. Based on the initial power flow distribution before the fault occurs, and combined with the steady-state thermal balance equations of the three-core cable, calculate the initial steady-state temperature of the conductor, inner lining, and armor layer of each branch cable at the preset fault occurrence time.

[0100] S2, Dynamic thermal circuit model construction, discretization, and linearization:

[0101] Based on the multi-layer radial structure of a three-core cable, a three-node equivalent transient thermal circuit model is established to characterize the dynamic temperature changes of each layer of the cable. This model describes the dynamic temperature evolution of the conductor layer, inner liner layer, and armor layer. The equivalent transient thermal circuit differential equation is discretized to obtain a transient temperature rise state equation that reflects the relationship between the temperature at the next moment and the temperature at the current moment. The McCormick envelope method is used to linearize the electro-thermal nonlinear coupling term between the current square and temperature in the transient temperature rise state equation due to conductor Joule losses, transforming it into a set of linear inequality constraints. A two-stage boundary dynamic contraction strategy is then used to solve the problem.

[0102] S3, Construction and solution of dynamic optimization model for fault reconstruction:

[0103] A fault reconfiguration dynamic optimization model is constructed with the objective function of minimizing the overall system operating cost (including the cost of purchasing electricity from the upstream grid, load shedding cost, switching operation cost, and distributed photovoltaic active curtailment cost). The linearized transient temperature rise state equation is embedded into the fault reconfiguration dynamic optimization model as a thermal safety verification constraint. By limiting the maximum temperature of the cable conductor within the reconstruction look-ahead time window to not exceed the maximum allowable temperature, the fault reconfiguration dynamic optimization model is solved in conjunction with the distribution network electrical constraints. The optimal fault reconfiguration topology scheme considering the thermal inertia safety boundary of the three-core cable is obtained, along with the corresponding load shedding, distributed photovoltaic curtailment, branch current, and temperature trajectory data.

[0104] The core of the active distribution network fault reconfiguration safety correction method provided in this embodiment is to perform physical safety verification on the topology self-healing scheme after a fault occurs. This requires the algorithm not only to seek the optimal switching action decision, but also to combine a three-core cable transient thermal circuit model to predict the temperature rise trajectory of each branch component in real time, so as to determine whether the reconfiguration scheme simultaneously meets physical thermal safety constraints and electrical operation requirements. The fault reconfiguration safety correction algorithm adopted in this invention is implemented through two stages: "data initialization" and "dynamic reconfiguration optimization". Its specific algorithm execution and logical decision-making process is as follows: Figure 2 As shown, the evolution and iterative convergence determination process of the coarse optimization stage, boundary dynamic shrinkage, and fine optimization stage are clearly illustrated. In dynamic reconstruction optimization, the combination of coarse optimization and fine optimization dynamic shrinkage effectively solves the convergence problem of solving complex electro-thermal coupling models containing discrete variables.

[0105] In active distribution networks, a fault set is typically defined as an abnormal disconnection event caused by a sudden fault in a branch element (such as a power cable). Power cables, as the main transmission carrier in the distribution network, play a crucial role in load transfer and distributed photovoltaic (PV) absorption during the reconfiguration process. This embodiment focuses on buried three-core cables as the core research object. The fault scenario can be specifically defined as follows: a three-core cable in a specific branch of the distribution network is taken out of service due to a fault, and the system achieves topology reconfiguration by optimizing and adjusting the states of tie switches and sectionalizing switches.

[0106] The analysis of fault scenarios aims to verify the safety indicators of the generated reconfiguration schemes and select the globally optimal solution. Traditional methods often use static current carrying capacity limits for "rigid" verification, neglecting the thermal inertia of cables due to their complex structure and buried environment. To ensure high physical accuracy of the analysis results, this embodiment first performs preprocessing to model the thermal parameters of the three-core cable and calculate steady-state initial values; then, a mixed integer quadratic constrained programming (MIQCP) model considering the transient temperature rise trajectory constraints of the cable is constructed and solved. In this way, this embodiment can dynamically depict the "overload-temperature rise" evolution process of the cable during reconfiguration, thereby maximizing the overload potential of the system while ensuring physical safety.

[0107] Example 2

[0108] A power distribution network correction control method considering the thermal characteristics of three-core cables, as described in Example 1, differs in that this example reconstructs the look-ahead time window. The time segment is divided into several time sections, with the time interval being the difference step size. Before performing the reconfiguration correction, it is necessary to first determine the physical parameters of the cable and the time of the fault occurrence. The initial state.

[0109] During cable operation, the AC resistance and Joule loss of the three-core cable conductors are strongly coupled with temperature, as shown in the following relationship:

[0110] (1)

[0111] (2)

[0112] In the formula, the subscript For the first A time segment; This refers to the number of cable cores. The reference DC resistance of the conductor at 20°C; This is the temperature coefficient of resistance, which is typically taken as 0.00393 1 / ℃ for copper conductors; AC resistance of conductors taking into account temperature effects; The square of the branch current; This represents the total Joule loss of the three-phase conductors of the cable.

[0113] In particular, and These are the skin effect coefficient and the proximity effect coefficient, respectively. To accurately characterize the AC loss of cables of different specifications, this embodiment... and Based on cable structure parameters and system frequency The calculation is performed using the following formula:

[0114] (3)

[0115] In the formula, and Temperature correction factors for skin effect and proximity effect (usually constant) are respectively. , ); The diameter of the conductor; This represents the conductor axis spacing. The corresponding formula can be used to obtain the appropriate value for different cable models. and Values.

[0116] Furthermore, substituting equation (1) into equation (2) reveals that the total Joule loss... It's actually about the square of the branch current. With conductor temperature The nonlinear function, which contains The coupling term is the core object of McCormick's linearization process.

[0117] To obtain accurate initial boundaries for transient temperature rise calculation, this embodiment uses the initial steady-state power flow distribution of the distribution network before the fault to obtain the initial current of each branch. At this point, the cable system reaches thermal equilibrium, and the derivative of the dynamic thermal equilibrium equation with respect to time is zero. The initial steady-state temperature can be obtained by solving the following set of steady-state thermal equilibrium equations. In step S1, the steady-state thermal equilibrium equations for the three-core cable are:

[0118] (4)

[0119] In the formula, The initial current of the branch before the fault occurred has a nominal value; This refers to the number of cable cores. , , , respectively, are the initial steady-state temperatures of the cable conductor, inner lining, and armor layer at the moment the fault occurs, in °C; The ambient temperature; AC resistance of conductors taking into account temperature effects; This refers to the loss of the three-phase insulating dielectric. , These are the sheath loss coefficient and the armor loss coefficient, respectively. These two coefficients characterize the proportion of the additional induced loss generated in the metal sheath and armor layer to the Joule loss of the conductor. To balance calculation accuracy and solution efficiency, the sheath loss coefficient of the three-core cable in the subsequent examples of this invention is... Taking a typical value of 0.03, the armor loss coefficient Take a typical value of 0.09; to These are the equivalent thermal resistances of the insulation layer, inner lining layer, armor layer, and soil layer, respectively.

[0120] Example 3

[0121] A power distribution network correction and control method considering the thermal characteristics of a three-core cable, as described in Example 2, differs in that, after a fault occurs and topology reconfiguration is performed, the branch current experiences a transient step jump. Due to the heat storage effect of the cable and its surrounding medium's heat capacity, the temperature of each layer exhibits significant transient thermal inertia. To accurately predict the temperature rise trajectory of the cable under a step current impact, this embodiment establishes a three-node equivalent transient thermal circuit model describing the dynamic temperature evolution of the cable's conductor layer, inner liner layer, and armor layer, as follows: Figure 3 The arrow indicates the direction of radial heat flow from the inside out.

[0122] In step S2, the original differential equation of the equivalent transient thermal circuit model, based on the law of heat conservation, can be expressed as:

[0123] (5)

[0124] In the formula, , , The temperatures of the conductor layer, inner liner layer, and armor layer at time t are respectively, in °C; The conductor Joule loss over time t; , , These are the effective heat capacities of conductor nodes, inner liner nodes, armor layers, and the external environment of the cable, respectively.

[0125] To facilitate time-series calculations in the optimization model, the implicit trapezoidal rule is used to discretize the differential equations of the equivalent transient thermal circuit model, resulting in the transient temperature rise state equation:

[0126] (6)

[0127] In the formula, the subscript Indicates the first The values ​​at each time segment; Let s be the difference step size. , , , respectively, are the temperatures of the conductor layer, inner liner layer, and armor layer at the t-th time segment, in °C; Let be the conductor loss at the t-th time segment; , These are the effective heat capacities of the conductor node and the inner liner node, respectively, after correction by the Van Wormer coefficient. This is the equivalent heat capacity of the armor layer and the external environment of the cable.

[0128] Example 4

[0129] A power distribution network correction and control method considering the thermal characteristics of a three-core cable, as described in Example 2, differs in that the effective heat capacity of each node is obtained by distributing and summarizing the heat capacity of each layer of the cable and a portion of the soil. The process is as follows:

[0130] First, calculate the volumetric heat capacity of each physical layer of the cable:

[0131] (7)

[0132] (8)

[0133] (9)

[0134] (10)

[0135] (11)

[0136] (12)

[0137] In the formula, , , , , , These are the heat capacities of the conductor, insulation layer, inner lining layer, armor layer, outer sheath, and effective soil layer, respectively. , , , , , These are the unit volume heat capacities of the conductor, insulation layer, inner lining layer, armor layer, outer sheath, and effective soil layer, respectively. The cross-sectional area of ​​the conductor; The diameter of the conductor; , , , These are respectively the insulation layer, inner lining layer, armor layer, and total outer diameter of the cable; The effective soil diameter, physically representing a characteristic diameter reflecting the extent of heat diffusion, is numerically determined based on a preset reconstruction look-ahead time window. And the thermal diffusion characteristics of the soil are determined, specifically satisfying:

[0138] (13)

[0139] In the formula, This is a preset reference period (e.g., 24 hours). This is the reference characteristic diameter determined based on the soil thermal diffusion characteristics under this reference period (e.g., a typical value of 211 mm). The current reconstruction lookahead time window length; in this embodiment, it is determined by the feature diameter. Delineate the effective soil heat dissipation boundary and heat storage range corresponding to the transient process.

[0140] To accurately simulate the temperature gradient and thermal storage characteristics inside the insulation layer, the Van Wormer coefficient was used. The thermal capacity of the insulating layer is distributed to adjacent thermal nodes, calculated using the following formula:

[0141] (14)

[0142] To effectively map the heat capacity of each physical layer into the three-node equivalent transient thermal path model, the Van Wormer coefficient allocation method is used to recombine the heat capacity, and the effective heat capacity of the conductor node, the inner liner node, and the armor layer node is calculated. , , The specific formula is as follows:

[0143] (15)

[0144] (16)

[0145] (17)

[0146] In the formula, The effective heat capacity of the conductor node, The effective heat capacity of the inner lining node, The effective heat capacity of the armor node;

[0147] Corresponding to the effective heat capacity, to The formulas for calculating the equivalent thermal resistance of the insulation layer, inner lining layer, armor layer, and soil layer are as follows:

[0148] (18)

[0149] (19)

[0150] (20)

[0151] (twenty one)

[0152] In the formula, , , , These are respectively the insulation, inner lining, armor layer, and soil thermal resistivity; The depth is the cable burial depth. It should be noted that the soil thermal resistance given in formula (21) is... This describes the thermal boundary resistance of the cable throughout its entire path in an underground environment. Considering the conservative requirements of power distribution network safety correction, this invention uses this steady-state thermal resistance as the thermal boundary during the transient process to ensure that the estimate of cable temperature rise within the reconstruction look-ahead time window is always within the safe envelope.

[0153] Example 5

[0154] A power distribution network correction control method considering the thermal characteristics of a three-core cable, as described in Example 4, differs in that the McCormick envelope method is used to address the nonlinear coupling term between the square of the current and temperature in the transient temperature rise state equation due to conductor Joule losses. Linearization is performed, specifically as follows:

[0155] Define nonlinear auxiliary variables The following set of linear inequalities are used to replace the non-convex product terms involving conductor losses in the transient temperature rise equation of state:

[0156] (twenty two)

[0157] In the formula, branch road At time step The per-unit value of the square of the current; and These are the maximum and minimum allowable values ​​for the conductor temperature, respectively. and These are the squares of the maximum and minimum currents of the branch, respectively; the transient temperature rise state equation is transformed into a linear constraint of the mixed integer quadratic constraint programming model (MIQCP) through linearization. and branch road The dynamic search boundary at different optimization stages, where Keep it at 0 to preserve the switching operation space for topology reconfiguration. A two-stage strategy is then used for dynamic contraction to reduce the relaxation error of the McCormick envelope.

[0158] Example 6

[0159] A power distribution network correction and control method considering the thermal characteristics of a three-core cable, as described in Example 5, except that... Figure 2 As shown, a two-stage boundary dynamic shrinkage strategy is used to solve the MIQCP model to balance efficiency and accuracy. The solution process is as follows:

[0160] (1) Coarse optimization stage: Set the square of the current in each branch. The initial search limit is the global maximum allowable value. The first round of optimization is performed to obtain the preliminary observation value of the square of the branch current.

[0161] (2) Fine optimization stage: Extract the maximum square value of the current in each branch observed in the first round, and then use the results from the second round of optimization. The search space is updated to the larger of a preset multiple of the observed maximum value and a preset safety lower limit, thereby constructing a more compact McCormick convex hull search space; the linear inequality set is regenerated based on the updated compact boundary and a second round of solving is performed to reduce linearization error.

[0162] In this embodiment, a preliminary reconstruction scheme and initial transient values ​​of current and temperature for each branch are obtained within an initial, relatively wide search boundary for auxiliary variables. Then, a fine-tuning optimization stage is entered. Based on the coarse optimization results, the lower limit of current is kept at 0 to allow sufficient space for topology switching, while the upper limit of the current search is dynamically shrunk to a tight neighborhood of the observed value, and the McCormick linearization constraints are updated accordingly. This two-stage evolution effectively narrows the envelope region of the nonlinear terms, significantly reducing the relaxation error caused by McCormick linearization. Thus, while ensuring computational speed, it ensures the physical accuracy of the reconstruction decision in describing the cable's thermal safety boundary, ultimately outputting the optimal topology and state parameters.

[0163] Example 7

[0164] A power distribution network correction and control method considering the thermal characteristics of three-core cables, as described in Example 6, differs in that, in step S3, the objective function of the fault reconfiguration dynamic optimization model is to minimize the overall operating cost of the power distribution network within the reconfiguration look-ahead time window, as expressed below:

[0165] (twenty three)

[0166] In the formula, To reconstruct the total operating cost of the system within the look-ahead time window; For the total set of time steps, The unit time step; , , and These are the unit price of electricity purchased from the distribution network to the upper-level power grid, the unit cost of load shedding compensation, the unit cost of distributed photovoltaic curtailment penalty (yuan / MW·h), and the cost of a single operation of the tie switch (yuan / time), and the values ​​are taken in accordance with the principle that ensuring power supply security takes precedence over operational economy; For the first The total active power (MW) injected into the distribution network substation (balance node) at each time step; and They are nodes At time step Active load shedding and nodes At time step Distributed photovoltaic curtailment (MW). branch road At time step The switch action variable is a binary variable. If the first... Step switch state compared If a step switch occurs, set the value to 1; otherwise, set the value to 0.

[0167] Example 8

[0168] A distribution network correction control method considering the thermal characteristics of three-core cables, as described in Example 7, differs in that, in order to balance the solution efficiency and convergence of the model, the branch resistance parameters used in this invention when constructing the branch power flow constraints of the distribution network are all constant total branch resistance values. The specific value is calculated by multiplying the unit length resistance of each cable specification by the actual laying length of the branch. This value remains constant during the topology reconstruction optimization process and does not fluctuate in real time with temperature or simulation period. This avoids introducing high-order nonlinear terms into the global second-order conical power flow optimization, ensuring the solvability of complex topology reconstruction problems. Simultaneously, to ensure the safety of the physical thermal boundary, the nonlinear characteristics of resistance fluctuation with temperature rise are strictly considered when solving the aforementioned transient temperature rise state equation for the cable.

[0169] The constraints of the fault reconfiguration dynamic optimization model include distribution network electrical topology constraints and cable physical boundary constraints considering thermal inertia. The distribution network electrical constraints are expressed using a branch power flow model based on the Big M method and second-order cone relaxation to ensure the electrical and topological feasibility of the reconfiguration scheme. The specific formulas are as follows:

[0170] (1) Node power balance constraints:

[0171] (twenty four)

[0172] The above equations represent the nodes respectively. At time step The active and reactive power balance takes into account branch losses, node loads, active and reactive load shedding, distributed photovoltaic output, and capacitor reactive power compensation.

[0173] (2) Branch voltage drop and switching logic coupling constraints:

[0174] (25)

[0175] This constraint describes the branch using the Big M method. Voltage drop and switching state The logical coupling relationship ensures that the voltage drop equation is satisfied only when the switch is closed.

[0176] (3) Second-order cone relaxation (SOCP) constraint:

[0177] (26)

[0178] This is a second-order cone relaxation (SOCP) constraint, used to transform the non-convex relationship of the product of the square of voltage and the square of current into a convex form, ensuring that the problem can be solved effectively.

[0179] (4) Radial constraints in network topology:

[0180] (27)

[0181] This constraint ensures that the reconfigured distribution network maintains a radial structure, meaning that the total number of closed branches should equal the total number of nodes minus 1.

[0182] (5) Switching operation limits and voltage safety constraints:

[0183] (28)

[0184] This is a switch action constraint, which limits the total number of global switch actions allowed within the reconstruction time window by summing the absolute values.

[0185] (29)

[0186] This is a node voltage safety constraint, which limits the voltage of each node to a preset safe operating range.

[0187] In the formula, For time step; Number the nodes; and All are branch road numbers; It is the set of all branches in the system; To study the set of all time steps within a given time period; For inflow node The set of branch paths; outflow node The set of branch paths; and Branch roads The first and last nodes; and They are the branch roads that flow through. Active and reactive power, and They are time steps Flowing through the branch road The active and reactive power together constitute the node. Power inflow and outflow terms; and Branch roads Resistance and reactance; branch road At time step The magnitude of the current; , , They are nodes , , At time step The square of the voltage amplitude; and They are nodes At time step The predicted values ​​of active and reactive loads; and They are nodes At time step The active and reactive load shedding quantities; For nodes At time step The upper limit of the predicted active power output of distributed photovoltaic power generation. Adjust its reactive power output; For nodes At time step Distributed photovoltaic curtailment; For sufficiently large positive numbers; The number of nodes; This represents the maximum total number of actions allowed globally in the active distribution network. branch road The maximum number of handovers allowed during the refactoring cycle; and Branch roads exist Time and The binary switch state variable at any given time; and These are the upper and lower limits of the allowable node voltage amplitude, respectively;

[0188] To ensure the physical feasibility of distributed photovoltaic (PV) systems participating in voltage optimization support, active distribution network operation constraints also include apparent capacity limitations for distributed PV inverters:

[0189] (30)

[0190] In the formula, For nodes At time step The upper limit of the predicted active power output of distributed photovoltaic power; For nodes At time step Distributed photovoltaic curtailment; For distributed photovoltaic inverters in time step The amount of reactive power output adjustment provided; For installation on the node The rated apparent capacity of the distributed photovoltaic inverter at the location;

[0191] The physical boundary constraints of the cable, taking thermal inertia into account, are described as follows:

[0192] (31)

[0193] In the formula, The branch obtained in real time through the transient temperature rise state equation of the cable At time step The conductor core temperature, This refers to the rated permissible temperature of the cable insulation material. This constraint replaces the rigid constraint on the static current carrying capacity rating in traditional reconfiguration, allowing the transient current of the branch to exceed the steady-state limit after reconfiguration, provided that the conductor temperature does not exceed the rated limit of the insulation material. This serves as the final physical boundary for safety. The constraint allows for branch lines. In the reconfiguration state, if a transient overcurrent occurs, as long as the temperature change process within the entire look-ahead time window does not exceed the maximum allowable temperature, the cable's inherent thermal inertia can be relied upon to safely exploit its dynamic transmission potential.

[0194] To verify the technical concept of this embodiment, specific calculation examples are provided below.

[0195] This embodiment uses an improved IEEE 33-node active distribution network as the verification system. Its baseline network topology and fault locations are as follows: Figure 4 As shown. The system's base voltage is 12.66kV, and all overhead lines in the system will be replaced with three-core cross-linked polyethylene (XLPE) underground cables. Based on current carrying capacity requirements, the cables are divided into 240mm sections. 2 120mm 2 70mm 2 and 50mm 2 The four specifications and models have the following maximum allowable operating temperatures for their insulation materials. The temperature is set to 90℃, the ambient temperature is 35℃, and the allowable range of node voltage is set to 0.9-1.1pu. Figure 4 In the diagram, the black numbers 1 to 33 represent the nodes of the active distribution network, and the gray numbers 1 to 37 represent the physical branches (including tie switch branches) in the system. Figure 4In the diagram, the geometric thickness and line type of each topological segment map to underground cable branches of different specifications, and the cross-sectional area decreases progressively from the main network to the terminal radial network. All cables are cross-linked polyethylene insulated steel-tape armored copper core power cables (YJV22 type, YJV22 is a commonly used cross-linked polyethylene insulated underground cable model), specifically including: YJV22-3×240mm located in the main network. 2 Cable (3×240mm) 2 This indicates the cross-sectional area of ​​the three-core cable and each individual conductor, and is located in the secondary trunk network as YJV22-3×120mm. 2 Cable, YJV22-3×70mm located at the end branch 2 With YJV22-3×50mm 2 Cables, and YJV22-3×70mm used as tie switch branches. 2 The electrical and thermal parameters of the cables and power grid are shown in Table 1.

[0196] Table 1 Electrical and thermal parameters of the power grid

[0197]

[0198] This embodiment sets up a fault self-healing scenario under the "nighttime peak heavy load" condition. Distributed photovoltaic (PV) devices are connected to nodes 15, 17, 18, 19, 21, 22, 25, and 33, with a total installed capacity of 8.8 MW. The fault scenario is set as follows: at time t=1, branch 7 goes offline due to a sudden fault, and the peak load of the entire network is approximately 7.36 MW. To guide the model to achieve an optimal balance between safe self-healing and economical operation, this embodiment sets various economic operating cost indicators: electricity purchase price of 500 yuan / MW·h, unit load shedding compensation cost of 50,000 yuan / MW·h, unit curtailment penalty cost of 3,000 yuan / MW·h, and single operation and maintenance cost of tie switch of 200 yuan / time. By comparing the safety correction strategy considering thermal inertia with the traditional rigid decision-making strategy based on static current limits, the technical advantages of this invention in improving power supply capacity under extreme conditions are evaluated.

[0199] Before performing dynamic reconfiguration optimization, the initial thermal state of the system before the fault needs to be solved using the steady-state thermal balance equations. Due to space limitations, Table 2 only lists the relevant parameters of some representative branches that bear the main power flow transmission and pressure transfer; the states of the remaining branches are calculated in the same way.

[0200] Table 2 Initial steady-state current and temperature of representative branches under two extreme operating conditions

[0201]

[0202] This simulation aims to verify the system's recovery capability under extreme heavy load pressure. The simulation period is set from 16:00 to 24:00, covering the evening peak hours of the distribution network. During this period, the net load of the entire network gradually increases with residential electricity demand, reaching a system peak of approximately 7.63MW around 18:00. Due to the natural decay of sunlight at night, the active power output of distributed photovoltaic power drops to zero after 19:00, and all the power required for load transfer is borne by the upstream substation through the reconfigured path. An N-1 fault is simulated to occur at 16:00, causing the main branch 7 to be forcibly disconnected.

[0203] Under this heavy load condition, due to the lack of a main power supply channel, any topology self-healing scheme must transfer a large amount of the affected load to the weakest branch at the end. To quantitatively evaluate the performance of this invention in improving self-healing resilience, a control scheme based on rigid static current carrying capacity verification (i.e.,...) is introduced. Figure 5 and Figure 6 The comparative scheme shown in the illustration ignores the dynamic equation of the cable transient thermal circuit constructed in this invention. Instead, it fixes the safety boundary based on the industry standard static rated current value corresponding to the cable model of each branch, which is a conservative control mode that does not consider the potential of the cable's transient thermal inertia. Under this heavy-load extreme fault scenario, because the system cannot find any global transfer topology path that can completely satisfy the requirement that the current of all branches in the network does not exceed the limit under this rigid current hard constraint, the comparative scheme is forced to choose to close the tie switch S33 and forcibly maintain the absolute safety of the electrical section through large-scale forced load shedding operations. Figure 6 As shown, during the entire reconfiguration time window, the control scheme could not utilize the overload window period for transition, resulting in a cumulative load shedding power of up to 9.373 MWh and an instantaneous load shedding power peak of 0.712 MW. This scheme not only has extremely high operating costs, but also cannot meet the power supply safety and recovery requirements under extreme operating conditions.

[0204] When implementing a reconfiguration decision, this invention successfully established a power transfer path after a fault by actively closing the contact switch S33. For example... Figure 5 As shown, although this action caused the current in the bottleneck branch 18 to surge to 227.29A instantaneously, the model did not blindly cut off the load. This is because the strategy of this invention changes the safety boundary of self-healing control from a "rigid current limit" to a "dynamic temperature constraint" based on the thermal circuit model. This is achieved by calculating and dynamically tracking the temperature trajectory of the branch over time in real time (i.e.,...). Figure 5The model, as shown in the legend ("temperature trajectory"), accurately assesses the actual thermal margin of the cable conductor during transient temperature rise, allowing for short-term overload below the thermal safety limit and enabling flexible release of the cable's transmission potential. Through proactive optimization, the model performs only minimal preventative load shedding (totaling only 0.473MW) when necessary, precisely controlling the core temperature of branch 18 to the safety threshold of 90.00℃. This is significantly better than the control scheme, which ignores the cable's transient thermal inertia and relies solely on rigid current boundaries (i.e.,...). Figure 5 (Comparative scheme in the previous version) The strategy of this invention directly uses the core temperature not exceeding its rated thermal limit as the safety verification boundary, successfully recovering 95.0% of the power outage losses, and maximizing the potential of cable transmission while ensuring thermal safety.

[0205] Table 3. Spatiotemporal distribution details of load shedding during evening peak heavy load fault recovery process

[0206] As shown in Table 3, under the strategy of this invention, the system only performed minimal preventative load shedding at critical nodes 17 and 18 in the disaster-stricken area, with cumulative load shedding amounts of 0.164MW and 0.309MW, respectively. When the conductor temperature of the bottleneck branch 18 rose due to reconfiguration and power transfer and precisely reached the safety threshold of 90℃, the model triggered a small load reduction in real time through electro-thermal coordination optimization logic, thus... Figure 5 The peak segment of the "temperature trajectory of this invention" operates close to the rated thermal safety limit of 90.0℃, thereby maximizing the recovery of the lost load while ensuring no thermal damage occurs. This decision-making process fully utilizes the thermal inertia potential of the cable, demonstrating the significant advantages of this invention in improving fault self-healing capabilities.

[0207] In addition, such as Figure 7 As shown, the overall network voltage remained within a safe range throughout the reconstruction process, with the lowest node voltage stabilizing at 0.917 pu. This is because, during the optimization process, this embodiment utilized the remaining reactive power regulation capacity of distributed photovoltaic inverters within the active distribution network to provide local voltage support, effectively offsetting the additional voltage drop caused by the release of thermal potential and current surges, thereby ensuring the coordinated balance of multi-dimensional constraints related to electricity, heat, and voltage.

[0208] The distribution network correction and control method proposed in this embodiment, which takes into account the thermal characteristics of three-core cables, restores the dynamic evolution law of line load and thermal response. Under the premise of ensuring that the insulation material does not suffer thermal damage and the node voltage does not exceed the limit, this method tracks the cable temperature rise trajectory in real time and makes reasonable use of the "transient safe overload window" of the cable during the fault reconfiguration process. This not only gives the distribution network a flexible margin for short-term overload operation but also significantly improves the system's load recovery capability and the absorption level of new energy sources under fault scenarios, providing scientific and efficient decision support for the self-healing control of active distribution networks.

[0209] Example 9

[0210] A power distribution network correction control system considering the thermal characteristics of a three-core cable, used to implement the method described in Example 8, characterized in that it includes:

[0211] The basic data and structural parameter acquisition module is configured to acquire the basic operating data of the active distribution network to be corrected and the radial physical structural parameters of the three-core cable, and input the reconstruction look-ahead simulation time window and preset fault scenarios.

[0212] The initial steady-state temperature distribution calculation module is configured to calculate the initial steady-state temperature of the conductor, inner lining and armor layer of each branch cable at the preset fault occurrence time, based on the initial steady-state power flow distribution of the active distribution network and combined with the steady-state thermal balance equations of the three-core cable.

[0213] The transient temperature rise prediction and optimization modeling module is configured to establish a three-node equivalent transient thermal circuit model of a three-core cable, and embed the discretized transient temperature rise state equation of the cable as a constraint into the dynamic optimization model of active distribution network fault reconfiguration. At the same time, the electro-thermal nonlinear coupling terms in the state equation are linearized by the McCormick envelope method, and the linearized search space is updated and optimized by a two-stage boundary dynamic shrinkage strategy.

[0214] The optimal reconfiguration scheme output module is configured to solve the dynamic optimization model of fault reconfiguration. Based on satisfying the electrical and topological constraints of the distribution network, it takes the maximum temperature of the cable conductor within the reconfiguration time window not exceeding the rated temperature limit of the insulation material as the safety physical boundary and outputs the optimal fault reconfiguration topology scheme.

[0215] Example 10

[0216] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the method described in any one of embodiments 1-8.

[0217] Example 11

[0218] A computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in any one of embodiments 1-8.

[0219] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A power distribution network correction and control method considering the thermal characteristics of a three-core cable, characterized in that, Includes the following steps: S1, Basic data acquisition and initial steady-state temperature calculation at the time of failure: Acquire basic operational data of the active distribution network, radial physical structural parameters and thermal parameters of the three-core cable; Based on the initial power flow distribution before the fault occurs, and combined with the steady-state thermal balance equations of the three-core cable, the initial steady-state temperatures of the cable conductors, inner lining, and armor layer of each branch at the preset fault occurrence time are calculated. S2, Dynamic thermal circuit model construction, discretization, and linearization: An equivalent transient thermal circuit model capable of characterizing the dynamic temperature changes of each layer of the cable is established; the equivalent transient thermal circuit differential equation is discretized to obtain a transient temperature rise state equation reflecting the relationship between the temperature at the next moment and the temperature at the current moment. The McCormick envelope method is used to linearize the electro-thermal nonlinear coupling terms in the transient temperature rise state equation, transforming them into a set of linear inequality constraints, and a two-stage boundary dynamic contraction strategy is used for solving them. The solution process using a two-stage boundary dynamic shrinkage strategy is as follows: (1) Coarse optimization stage: Set the square of the current in each branch. The initial search limit is the global maximum allowable value. The first round of optimization is performed to obtain the preliminary observation value of the square of the branch current. (2) Fine optimization stage: Extract the maximum square value of the current in each branch observed in the first round, and then use the results from the second round of optimization. The search space is updated to the larger of a preset multiple of the observed maximum value and a preset safety lower limit value, thereby constructing a more compact McCormick convex hull search space; the linear inequality system is regenerated based on the updated compact boundary and a second round of solving is performed to reduce linearization error; S3, Construction and solution of dynamic optimization model for fault reconstruction: A fault reconfiguration dynamic optimization model is constructed with the objective function of minimizing the overall system operating cost. The linearized transient temperature rise state equation is embedded into the fault reconfiguration dynamic optimization model as a thermal safety verification constraint. By limiting the maximum temperature of the cable conductor within the reconfiguration look-ahead time window to not exceed the maximum allowable temperature, the fault reconfiguration dynamic optimization model is solved in combination with the distribution network electrical constraints. The optimal fault reconfiguration topology scheme considering the thermal inertia safety boundary of the three-core cable is obtained, along with the corresponding load shedding, distributed photovoltaic curtailment, branch current, and temperature trajectory data.

2. The power distribution network correction and control method considering the thermal characteristics of a three-core cable according to claim 1, characterized in that, In step S1, the steady-state thermal equilibrium equations for the three-core cable are: （4） In the formula, The initial current of the branch before the fault occurred has a nominal value; This refers to the number of cable cores. , , , respectively, are the initial steady-state temperatures (°C) of the cable conductor, inner liner, and armor layer at the moment the fault occurs; Ambient temperature; AC resistance of conductors taking into account temperature effects; This refers to the loss of the three-phase insulating dielectric. , These are the sheath loss coefficient and the armor loss coefficient, respectively. to These are the equivalent thermal resistances of the insulation layer, inner lining layer, armor layer, and soil layer, respectively.

3. The power distribution network correction and control method considering the thermal characteristics of a three-core cable according to claim 2, characterized in that, In step S2, the equivalent transient thermal circuit model is expressed as: （5） In the formula, , , The temperatures of the conductor layer, inner liner layer, and armor layer at time t are respectively, in °C; The conductor Joule loss over time t; , , These are the effective heat capacities of conductor nodes, inner liner nodes, armor layers, and the external environment of the cable, respectively. The differential equations of the equivalent transient thermal circuit model are discretized using the implicit trapezoidal rule to obtain the transient temperature rise state equation: （6） In the formula, Let s be the difference step size.

4. The power distribution network correction and control method considering the thermal characteristics of a three-core cable according to claim 3, characterized in that, The effective heat capacity of each node is obtained by distributing and summing the heat capacity of each layer of the cable and part of the soil. The process is as follows: First, calculate the volumetric heat capacity of each physical layer of the cable: （7） （8） （9） （10） （11） （12） In the formula, , , , , , These are the heat capacities of the conductor, insulation layer, inner lining layer, armor layer, outer sheath, and effective soil layer, respectively. , , , , , These are the unit volume heat capacities of the conductor, insulation layer, inner lining, armor layer, outer sheath, and effective soil layer, respectively. The cross-sectional area of ​​the conductor; The diameter of the conductor; , , , These are respectively the insulation layer, inner lining layer, armor layer, and total outer diameter of the cable; The effective soil diameter, physically representing a characteristic diameter reflecting the extent of heat diffusion, is numerically determined based on a preset reconstruction look-ahead time window. And the thermal diffusion characteristics of the soil are determined, specifically satisfying: （13） In the formula, This is the preset reference period; This is the reference characteristic diameter determined based on the soil thermal diffusion characteristics under this reference period; The current reconstruction lookahead time window length; To accurately simulate the temperature gradient and thermal storage characteristics inside the insulation layer, the Van Wormer coefficient was used. The thermal capacity of the insulating layer is distributed to adjacent thermal nodes, calculated using the following formula: （14） To effectively map the heat capacity of each physical layer into the equivalent transient thermal circuit model, the Van Wormer coefficient allocation method is used to recombine the heat capacity, and the effective heat capacity of the conductor node, the inner liner node, and the armor layer node is calculated. , , The specific formula is as follows: （15） （16） （17） In the formula, The effective heat capacity of the conductor node, The effective heat capacity of the inner lining node, The effective heat capacity of the armor node; to The formulas for calculating the equivalent thermal resistance of the insulation layer, inner lining layer, armor layer, and soil layer are as follows: （18） （19） （20） （21） In the formula, , , , These are respectively the insulation, inner lining, armor layer, and soil thermal resistivity; The depth at which the cable is buried.

5. The power distribution network correction and control method considering the thermal characteristics of a three-core cable according to claim 3, characterized in that, The McCormick envelope method is used to analyze the nonlinear coupling term between the square of the current and temperature in the transient temperature rise equation of state due to conductor Joule losses. Linearization is performed, specifically as follows: Define nonlinear auxiliary variables The following set of linear inequalities are used to replace the non-convex product terms involving conductor losses in the transient temperature rise equation of state: （22） In the formula, branch road At time step The per-unit value of the square of the current; and These are the maximum and minimum allowable values ​​for the conductor temperature, respectively. and These are the squares of the maximum and minimum currents of the branch, respectively; the transient temperature rise state equation is transformed into a linear constraint of a mixed integer quadratic constraint programming model through linearization.

6. The power distribution network correction and control method considering the thermal characteristics of a three-core cable according to claim 5, characterized in that, In step S3, the objective function of the fault reconfiguration dynamic optimization model is to minimize the overall operating cost of the distribution network within the reconfiguration look-ahead time window, as expressed below: （23） In the formula, To reconstruct the total operating cost of the system within the look-ahead time window; For the total set of time steps, The unit time step; , , and These are the unit price of electricity purchased by the distribution network from the upper-level power grid, the unit cost of load shedding compensation, the unit cost of distributed photovoltaic curtailment penalty, and the cost of a single operation of the tie switch; For the first The total active power injected into the distribution network substation at each time step; and They are nodes At time step Active load shedding and nodes At time step Distributed photovoltaic curtailment; branch road At time step The switch action variable is a binary variable. If the first... Step switch state compared If a step switch occurs, set the value to 1; otherwise, set the value to 0.

7. The power distribution network correction and control method considering the thermal characteristics of a three-core cable according to claim 6, characterized in that, The electrical constraints of the distribution network are expressed using a branch power flow model based on the Big M method and second-order cone relaxation to ensure the electrical and topological safety and feasibility of the reconfiguration scheme. The specific formulas are as follows: (1) Node power balance constraints: （24） (2) Branch voltage drop and switching logic coupling constraints: （25） (3) Second-order cone relaxation constraint: （26） (4) Radial constraints in network topology: （27） (5) Switching operation limits and voltage safety constraints: （28） （29） In the formula, For time step; Number the nodes; and All are branch road numbers; It is the set of all branches in the system; To study the set of all time steps within a given time period; For inflow node The set of branch paths; outflow node The set of branch paths; and Branch roads The first and last nodes; and They are the branch roads that flow through. Active and reactive power, and They are time steps Flowing through the branch road The active and reactive power together constitute the node. Power inflow and outflow terms; and Branch roads Resistance and reactance; branch road At time step The magnitude of the current; , , They are nodes , , At time step The square of the voltage amplitude; and They are nodes At time step The predicted values ​​of active and reactive loads; and They are nodes At time step The active and reactive load shedding quantities; For nodes At time step The upper limit of the predicted active power output of distributed photovoltaic power generation. Adjust its reactive power output; For nodes At time step Distributed photovoltaic curtailment; For sufficiently large positive numbers; The number of nodes; This represents the maximum total number of actions allowed globally in the active distribution network. branch road The maximum number of handovers allowed during the refactoring cycle; and Branch roads exist Time and The binary switch state variable at any given time; and These are the upper and lower limits of the allowable node voltage amplitude, respectively; To ensure the physical feasibility of distributed photovoltaic (PV) systems participating in voltage optimization support, active distribution network operation constraints also include apparent capacity limitations for distributed PV inverters: （30） In the formula, For nodes At time step The upper limit of the predicted active power output of distributed photovoltaic power generation; For nodes At time step Distributed photovoltaic curtailment; For distributed photovoltaic inverters in time step The amount of reactive power output adjustment provided; For installation on the node The rated apparent capacity of the distributed photovoltaic inverter at the location; The physical boundary constraints of the cable, taking thermal inertia into account, are described as follows: （31） In the formula, The branch obtained in real time through the transient temperature rise state equation of the cable At time step The conductor core temperature, This refers to the rated permissible temperature of the cable insulation material.

8. A power distribution network correction control system considering the thermal characteristics of a three-core cable, used to implement the power distribution network correction control method considering the thermal characteristics of a three-core cable as described in any one of claims 1-7, characterized in that, include: The basic data and structural parameter acquisition module is configured to acquire the basic operating data of the active distribution network to be corrected and the radial physical structural parameters of the three-core cable, and input the reconstruction look-ahead simulation time window and preset fault scenarios. The initial steady-state temperature distribution calculation module is configured to calculate the initial steady-state temperature of the conductor, inner lining and armor layer of each branch cable at the preset fault occurrence time, based on the initial steady-state power flow distribution of the active distribution network and combined with the steady-state thermal balance equations of the three-core cable. The transient temperature rise prediction and optimization modeling module is configured to establish a three-node equivalent transient thermal circuit model of a three-core cable, and embed the discretized transient temperature rise state equation of the cable as a constraint into the dynamic optimization model of active distribution network fault reconfiguration. At the same time, the electro-thermal nonlinear coupling terms in the state equation are linearized by the McCormick envelope method, and the linearized search space is updated and optimized by a two-stage boundary dynamic shrinkage strategy. The optimal reconfiguration scheme output module is configured to solve the dynamic optimization model of fault reconfiguration. Based on satisfying the electrical and topological constraints of the distribution network, it takes the maximum temperature of the cable conductor within the reconfiguration time window not exceeding the rated temperature limit of the insulation material as the safety physical boundary and outputs the optimal fault reconfiguration topology scheme.

9. An electronic device, characterized in that, The method includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the processor executes the computer instructions, the power distribution network correction control method taking into account the thermal characteristics of a three-core cable as described in any one of claims 1-7 is executed.

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