A multi-voltage grading power grid dynamic load recovery method considering time-varying cold load starting

Abstract

The application discloses a kind of considering time-varying cold load start-up multi-voltage grading power grid dynamic load recovery method, comprising: establishing time-varying cold load start-up model based on lower triangular coefficient matrix;Multi-voltage grading power grid dynamic load recovery model is constructed, and constraint condition is comprehensively considered, and mixed integer second order cone programming model is formed;Solve mixed integer second order cone programming model under coarse-grained time scale, obtain the coarse-grained mechanical topology sequence of global optimum;Mechanical topology sequence under coarse-grained time scale is mapped to fine-grained time scale by zero order, in the case where fixed topology, transient cold load anti-inrush check is carried out, and the final dynamic load recovery strategy is output.The application can effectively avoid the risk of overestimation and out-of-limit caused by static load assumption, while significantly reducing the calculation burden of large-scale multi-voltage grading power grid recovery model, and improves the recovery efficiency and physical safety of distribution network under extreme disaster.

Description

Technical Field

[0001] This invention belongs to the field of power grids and relates to the flexible optimization technology of smart distribution networks. Specifically, it relates to a dynamic load recovery method for multi-voltage level distribution networks that takes into account the start-up of time-varying cold loads. Background Technology

[0002] In recent years, the frequency and intensity of extreme weather events such as typhoons, rainstorms, and cold waves have been increasing, posing a serious threat to the safe operation of power distribution networks. How to quickly restore critical loads and improve the system's self-healing capabilities after disasters has become an important requirement for the safe operation of modern power distribution networks.

[0003] Traditional distribution network restoration primarily relies on network reconfiguration, distributed generation, and mobile emergency power supplies, which struggle to provide sufficient power transfer flexibility and voltage support when facing complex faults. With the development of power electronics technology, smart soft switching (SOP) has provided an effective means to improve the load recovery capability of distribution networks. However, existing technologies still have the following significant drawbacks:

[0004] (1) Current research on SOP-assisted distribution network restoration mainly focuses on single voltage levels, lacking exploration of the potential for cross-voltage level collaborative restoration between distribution transformers, medium-voltage feeders and low-voltage areas;

[0005] (2) Existing technologies mostly adopt traditional symmetrical SOP structures. In post-disaster recovery, the power support requirements between feeders are extremely unbalanced. Symmetrical SOPs face the bottleneck of limited capacity of heavy-load ports and idle capacity of light-load ports, which limits the overall recovery performance of the system.

[0006] (3) Most existing research on distribution network restoration adopts static load models. However, actual distribution networks contain a large number of temperature-controlled loads (TCLs), which lose their diversity coefficients after a long power outage, resulting in a significant surge in cold load start-up (CLPU) at the beginning of power restoration. Ignoring this phenomenon will seriously underestimate the actual load demand for restoration, leading to line overload or voltage collapse; if the traditional delay exponential model (DEM) is used, it will overly pessimistically limit the restoration strategy.

[0007] (4) When considering multiple voltage levels, M-SOP operation and dynamic evolution of CLPU, the system cascade recovery model presents itself as a large-scale mixed integer nonlinear optimization problem, which faces a serious dimensionality curse. Existing commercial solvers are unable to provide feasible solutions within the time required for post-disaster emergency response. Summary of the Invention

[0008] Purpose of the invention: In order to overcome the shortcomings of the existing technology, a dynamic load restoration method for multi-voltage level distribution networks that considers the start-up of time-varying cold loads is provided. This method can effectively avoid the risk of overestimation of load and exceeding limits caused by static load assumptions, while significantly reducing the computational burden of large-scale multi-voltage level distribution network restoration models and improving the restoration efficiency and physical safety of distribution networks under extreme disasters.

[0009] Technical Solution: To achieve the above objectives, this invention provides a dynamic load restoration method for multi-voltage level distribution networks that considers time-varying cold load initiation, comprising the following steps:

[0010] S1: Establish a time-varying cold load start-up (CLPU) model based on the lower triangular coefficient matrix to quantify the dynamic impact of outage duration and recovery time on load surges;

[0011] S2: Construct a dynamic load recovery model for a multi-voltage-level distribution network, and comprehensively consider the constraints to form a mixed integer second-order cone programming (MISOCP) model with the main objective of maximizing the recovery load;

[0012] S3: The three-stage relaxation-induction-polishing acceleration algorithm (TS-RIPA) is used to solve the mixed integer second-order cone programming model at a coarse-grained time scale to obtain the globally optimal coarse-grained mechanical topology sequence;

[0013] S4: Map the mechanical topology sequence at the coarse-grained time scale to the fine-grained time scale using zero-order hold-up mapping. Under the condition of fixed topology, solve the pure time-series load high-frequency switching and equipment scheduling model, perform transient cold load surge protection verification, and output the final dynamic load recovery strategy.

[0014] Furthermore, the establishment of the time-varying cold load start-up model in step S1 includes: characterizing the time-varying load surge characteristics caused by the loss of diversity coefficients of the constant temperature control load after a long power outage through a lower triangular coefficient matrix, and constructing surge protection safety constraints.

[0015] Furthermore, the process of establishing the time-varying cooling load start-up model in step S1 includes:

[0016] The timing logic constraints are established as follows:

[0017]

[0018]

[0019]

[0020] Construct the lower triangular coefficient matrix The spatiotemporal dynamic evolution characteristics of cold load startup are described as follows:

[0021]

[0022] Among them, diagonal elements Indicates the corresponding power outage duration The initial surge peak multiplier; the first The column represents the corresponding subsequent load decay trajectory;

[0023] The actual active and reactive power requirements of the nodes are calculated as follows:

[0024]

[0025]

[0026] in, For discrete load recovery indicator variables, For a set of nodes, For time sets; to prevent voltage collapse caused by the superposition of surges during cold load startup, the surge protection safety constraints limiting the single-step load recovery amplitude are as follows:

[0027]

[0028] in, This is an indicator variable for load recovery actions.

[0029] Furthermore, in step S2, the objective function of the multi-voltage level distribution network dynamic load recovery model comprehensively considers maximizing the total restored load, minimizing distributed generation curtailment, minimizing main grid injected power, and minimizing network losses. The objective function is expressed as follows:

[0030]

[0031] The calculation formulas for each sub-objective are as follows:

[0032]

[0033] in, The target weight coefficient; For node load recovery state variables, Rated active load for nodes; and These represent the available active power and actual output of the distributed power source, respectively. This contributes to the mainnet. This refers to internal losses within the standard operating procedure (SOP). The replacement variable is the square of the branch current. This is the branch resistance. To restore the total rated load, This is a reduction in active power for DG. Injecting positive energy into the mainnet and These are the internal losses of the SOP and the network line losses, respectively.

[0034] Furthermore, the constraints in step S2 include multi-voltage level distribution network topology reconfiguration constraints, multi-layer flexible interconnection equipment operation constraints, linearized DistFlow power flow constraints, and system operation safety constraints.

[0035] Furthermore, in step S2:

[0036] The topology reconfiguration constraints for multi-voltage level distribution networks, constructed based on a virtual power flow model, are as follows:

[0037] The fault isolation constraints are as follows:

[0038]

[0039] The radial topology constraints of the multi-voltage level network are as follows:

[0040]

[0041] The constraints to prevent closed loops from forming between multiple SOP ports are as follows:

[0042]

[0043] The virtual power flow balance constraints are as follows:

[0044]

[0045]

[0046] The constraint that virtual power flow is only allowed to flow in closed branches is as follows:

[0047]

[0048] In the formula, In branch connection state, The virtual root node status for the SOP port. As slack variables, For the virtual power flow of the branch, M is a sufficiently large positive integer;

[0049] Operational constraints for multi-layer flexible interconnection devices include unified modeling of medium-voltage asymmetrical multiplexed smart soft switches (M-SOP) and low-voltage symmetrical smart soft switches (LV-SOP), as detailed below:

[0050] The apparent power capacity uniform operating constraints are as follows:

[0051]

[0052] The active power conservation constraint considering internal conversion losses is as follows:

[0053]

[0054] For asymmetric M-SOP, the uniqueness allocation constraint of the VSC module is as follows:

[0055]

[0056] The dynamic capacity matching mapping constraints for M-SOP ports are as follows:

[0057]

[0058] In the formula, and Inject active and reactive power into the SOP port. For port capacity, The loss coefficient is... The binary selection matrix allocated to the VSC module. This refers to the module's rated capacity.

[0059] The DistFlow power flow constraint is linearized, incorporating both on-load tap-changing transformers (OLTCs) and network losses into the calculation, as detailed below:

[0060] The active power balance constraints at the nodes are as follows:

[0061]

[0062] Among them, transformer ratio parameters The definition is as follows:

[0063]

[0064] The reactive power balance constraints at the nodes are as follows:

[0065]

[0066] The voltage drop constraints for conventional circuits within the layer are as follows:

[0067]

[0068] The voltage drop constraint for a cross-voltage level transformer branch containing an OLTC is as follows:

[0069]

[0070] The OLTC discrete ratio adjustment constraints are as follows:

[0071]

[0072] In the formula, and For the active and reactive power flow of the line; The square of the node voltage magnitude; For OLTC discrete voltage turns ratio; For OLTC gear step size variables;

[0073] System operational safety constraints include node voltage, branch thermal capacity, and distributed generation operating envelope boundary constraints, as detailed below:

[0074] The node voltage magnitude constraints and root node voltage settings are as follows:

[0075]

[0076] The apparent power thermal limit constraint of the branch is as follows:

[0077]

[0078] The active power output constraints of distributed generation (DG) are as follows:

[0079]

[0080] The reactive power factor limits for distributed generation are as follows:

[0081]

[0082] The apparent power capacity limitations of distributed generation are as follows:

[0083] .

[0084] Furthermore, in step S3, a three-stage relaxation-induction-polishing acceleration algorithm is adopted. At a coarse-grained time scale, the constructed model is continuously relaxed, the auxiliary induced function is extracted as a pseudo gradient, and it is transformed into an auxiliary penalty term and added to the polishing objective function to solve for the globally optimal coarse-grained mechanical topology sequence.

[0085] Furthermore, the execution process of the three-stage relaxation-induction-polishing acceleration algorithm in step S3 includes:

[0086] A1: Topology relaxation: Reducing the time-series load scheduling variables Continuous relaxation, preserving mechanical topological variables The discrete properties of the object, with the objective of maximizing only the total restored active power load. Solving under the given conditions yields the globally optimal mechanical topology sequence. as follows:

[0087]

[0088] A2: Auxiliary Induction Function (AIF) Extraction: By fixing the mechanical topology constant, the load variables in the relaxed state are obtained by solving a continuous linear programming problem. The AIF factor, which serves as a pseudo-gradient, is extracted according to the following formula. :

[0089]

[0090] A3: Integer Polishing: Recovery The discrete integer properties of the AIF factor are used as an auxiliary penalty term to construct the polishing objective function, which quickly outputs a high-quality coarse-grained recovery sequence as follows:

[0091]

[0092] .

[0093] Further, step S4 includes:

[0094] B1: Zero-order time-scale-preserving mapping: mapping coarse-grained time domains Subdivided into fine-grained time-domain sets The determined mechanical topology is rigidly translated to a fine-grained time axis using zero-order hold logic as follows:

[0095]

[0096] B2: Fine-grained Mixed Integer Linear Programming (MILP) Execution: Under a fixed mechanical topology, optimization is performed on the load switch operation and the dynamic capacity matching matrix of the M-SOP module. The objective function is updated to collaboratively maximize load recovery and smooth DG output as follows:

[0097]

[0098] While solving the above model, a strict extreme constraint on transient cooling load surge protection is imposed at a fine-grained time section, as expressed below:

[0099]

[0100] This results in a batch-staggered optimal recovery solution with surge protection safety guarantees.

[0101] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0102] 1. This invention overcomes the shortcomings of poor coordination capabilities in single-voltage-level recovery strategies, achieving deep coordination across voltage levels. This invention constructs a multi-voltage-level dynamic recovery framework comprising on-load tap-changing transformers (OLTCs) in substations, medium-voltage multi-port multiplexed intelligent soft switches (M-SOPs), and low-voltage intelligent soft switches (LV-SOPs). Through the local peak reduction and imbalance smoothing effects of the low-voltage SOPs at the network edge, the net power compensation burden on the medium-voltage network is effectively reduced, thereby releasing the capacity margin of the medium-voltage M-SOPs and significantly improving the power support capability across voltage levels and the recovery rate of critical loads throughout the system.

[0103] 2. This invention overcomes the bottleneck of limited port capacity and idle capacity in traditional symmetrical SOPs, improving power transfer flexibility under extreme operating conditions. This invention introduces an asymmetrical intelligent soft switch (M-SOP) and establishes its dynamic capacity matching constraints. In situations where the power support demand of feeders is extremely unbalanced after a disaster, the M-SOP can dynamically allocate its large-capacity ports to heavily loaded or faulty feeders, accurately matching actual recovery needs, avoiding the capacity bottleneck caused by the symmetrical structure, and significantly shortening system recovery time.

[0104] 3. This invention overcomes the safety hazards caused by neglecting Cold Load Start (CLPU) in static load models, ensuring physical safety during the recovery process. This invention innovatively establishes a time-varying cold load start model based on a lower triangular coefficient matrix, accurately quantifying the dynamic impact of outage duration and recovery time on load surges. It avoids the risks of line thermal overload and severe voltage collapse caused by ignoring CLPU; it also avoids resource idleness caused by the overly conservative traditional Delay Exponential Model (DEM), achieving rapid and safe load switching while ensuring that the voltage at all nodes remains within a safe range.

[0105] 4. This invention overcomes the challenge of rapidly solving large-scale multi-voltage-level spatiotemporal coupled models, meeting the timeliness requirements of post-disaster emergency response. Addressing the dimensionality curse caused by the resulting large-scale mixed-integer second-order cone programming (MISOCP), this invention proposes a three-stage relaxation-induced-polishing acceleration algorithm (TS-RIPA). This algorithm decouples coarse-grained topology optimization from fine-grained load surge protection verification in both time and space, ensuring global optimization accuracy and physical feasibility while increasing the solution speed by more than 10 times compared to traditional commercial solvers such as CPLEX. It can even output the optimal strategy within minutes in large-scale distribution networks with hundreds of nodes, demonstrating strong engineering applicability and scalability. Attached Figure Description

[0106] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0107] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0108] Example 1:

[0109] like Figure 1 As shown in the figure, this embodiment provides a dynamic load restoration method for multi-voltage level distribution networks that considers the start-up of time-varying cold loads, including the following steps:

[0110] S1: Establish a time-varying cold load start-up (CLPU) model based on the lower triangular coefficient matrix to quantify the dynamic impact of outage duration and recovery time on load surges;

[0111] The establishment of the time-varying cold load start-up model includes: characterizing the time-varying load surge characteristics caused by the loss of diversity coefficients of the constant temperature control load after a long power outage through the lower triangular coefficient matrix, and constructing surge protection safety constraints.

[0112] The process of establishing a time-varying cooling load start-up model includes:

[0113] The timing logic constraints are established as follows:

[0114]

[0115]

[0116]

[0117] Construct the lower triangular coefficient matrix The spatiotemporal dynamic evolution characteristics of cold load startup are described as follows:

[0118]

[0119] Among them, diagonal elements Indicates the corresponding power outage duration The initial surge peak multiplier; the first The column represents the corresponding subsequent load decay trajectory;

[0120] The actual active and reactive power requirements of the nodes are calculated as follows:

[0121]

[0122]

[0123] in, For discrete load recovery indicator variables, For a set of nodes, For time sets; to prevent voltage collapse caused by the superposition of surges during cold load startup, the surge protection safety constraints limiting the single-step load recovery amplitude are as follows:

[0124]

[0125] in, This is an indicator variable for load recovery actions.

[0126] S2: Construct a dynamic load recovery model for a multi-voltage-level distribution network, and comprehensively consider the constraints to form a mixed integer second-order cone programming (MISOCP) model with the main objective of maximizing the recovery load;

[0127] The objective function of the dynamic load recovery model for multi-voltage distribution networks comprehensively considers maximizing total restored load, minimizing distributed generation curtailment, minimizing main grid injected power, and minimizing network losses. The objective function is expressed as follows:

[0128]

[0129] The calculation formulas for each sub-objective are as follows:

[0130]

[0131] in, The target weight coefficient; For node load recovery state variables, Rated active load for nodes; and These represent the available active power and actual output of the distributed power source, respectively. This contributes to the mainnet. This refers to internal losses within the standard operating procedure (SOP). The replacement variable is the square of the branch current. This is the branch resistance. To restore the total rated load, This is a reduction in active power for DG. Injecting positive energy into the mainnet and These are the internal losses of the SOP and the network line losses, respectively.

[0132] The constraints include multi-voltage level distribution network topology reconfiguration constraints, multi-layer flexible interconnection equipment operation constraints, linearized DistFlow power flow constraints, and system operation safety constraints, as detailed below:

[0133] The topology reconfiguration constraints for multi-voltage level distribution networks, constructed based on a virtual power flow model, are as follows:

[0134] The fault isolation constraints are as follows:

[0135]

[0136] The radial topology constraints of the multi-voltage level network are as follows:

[0137]

[0138] The constraints to prevent closed loops from forming between multiple SOP ports are as follows:

[0139]

[0140] The virtual power flow balance constraints are as follows:

[0141]

[0142]

[0143] The constraint that virtual power flow is only allowed to flow in closed branches is as follows:

[0144]

[0145] In the formula, In branch connection state, The virtual root node status for the SOP port. As slack variables, For branch virtual trends, It is a sufficiently large positive number;

[0146] Operational constraints for multi-layer flexible interconnection devices include unified modeling of medium-voltage asymmetrical multiplexed smart soft switches (M-SOP) and low-voltage symmetrical smart soft switches (LV-SOP), as detailed below:

[0147] The apparent power capacity uniform operating constraints are as follows:

[0148]

[0149] The active power conservation constraint considering internal conversion losses is as follows:

[0150]

[0151] For asymmetric M-SOP, the uniqueness allocation constraint of the VSC module is as follows:

[0152]

[0153] The dynamic capacity matching mapping constraints for M-SOP ports are as follows:

[0154]

[0155] In the formula, and Inject active and reactive power into the SOP port. For port capacity, The loss coefficient is... The binary selection matrix allocated to the VSC module. This refers to the module's rated capacity.

[0156] The DistFlow power flow constraint is linearized, incorporating both on-load tap-changing transformers (OLTCs) and network losses into the calculation, as detailed below:

[0157] The active power balance constraints at the nodes are as follows:

[0158]

[0159] Among them, transformer ratio parameters The definition is as follows:

[0160]

[0161] The reactive power balance constraints at the nodes are as follows:

[0162]

[0163] The voltage drop constraints for conventional circuits within the layer are as follows:

[0164]

[0165] The voltage drop constraint for a cross-voltage level transformer branch containing an OLTC is as follows:

[0166]

[0167] The OLTC discrete ratio adjustment constraints are as follows:

[0168]

[0169] In the formula, and For the active and reactive power flow of the line; The square of the node voltage magnitude; For OLTC discrete voltage turns ratio; For OLTC gear step size variables;

[0170] System operational safety constraints include node voltage, branch thermal capacity, and distributed generation operating envelope boundary constraints, as detailed below:

[0171] The node voltage magnitude constraints and root node voltage settings are as follows:

[0172]

[0173] The apparent power thermal limit constraint of the branch is as follows:

[0174]

[0175] The active power output constraints of distributed generation (DG) are as follows:

[0176]

[0177] The reactive power factor limits for distributed generation are as follows:

[0178]

[0179] The apparent power capacity limitations of distributed generation are as follows:

[0180] .

[0181] S3: The three-stage relaxation-induction-polishing acceleration algorithm (TS-RIPA) is used to solve the mixed integer second-order cone programming model at a coarse-grained time scale to obtain the globally optimal coarse-grained mechanical topology sequence;

[0182] In this embodiment, a three-stage relaxation-induction-polishing acceleration algorithm is adopted. At a coarse-grained time scale, the constructed model is continuously relaxed, the auxiliary induced function is extracted as a pseudo gradient, and it is transformed into an auxiliary penalty term and added to the polishing objective function. The globally optimal coarse-grained mechanical topology sequence is obtained by solving the algorithm.

[0183] The execution process of the three-stage relaxation-induction-polishing acceleration algorithm includes:

[0184] A1: Topology relaxation: Reducing the time-series load scheduling variables Continuous relaxation, preserving mechanical topological variables The discrete properties of the object, with the objective of maximizing only the total restored active power load. Solving under the given conditions yields the globally optimal mechanical topology sequence. as follows:

[0185]

[0186] A2: Auxiliary Induction Function (AIF) Extraction: By fixing the mechanical topology constant, the load variables in the relaxed state are obtained by solving a continuous linear programming problem. The AIF factor, which serves as a pseudo-gradient, is extracted according to the following formula. :

[0187]

[0188] A3: Integer Polishing: Recovery The discrete integer properties of the AIF factor are used as an auxiliary penalty term to construct the polishing objective function, which quickly outputs a high-quality coarse-grained recovery sequence as follows:

[0189]

[0190] .

[0191] S4: Map the mechanical topology sequence at the coarse-grained time scale to the fine-grained time scale using zero-order hold-up mapping. Under the condition of fixed topology, solve the pure time-series load high-frequency switching and equipment scheduling model (MILP model), perform transient cold load surge protection verification, and output the final dynamic load recovery strategy.

[0192] Step S4 includes:

[0193] B1: Zero-order time-scale-preserving mapping: subdividing the coarse-grained time domain T into a set of fine-grained time domains. The determined mechanical topology is rigidly translated to a fine-grained time axis using zero-order hold logic as follows:

[0194]

[0195] B2: Fine-grained Mixed Integer Linear Programming (MILP) Execution: Under a fixed mechanical topology, optimization is performed on the load switch operation and the dynamic capacity matching matrix of the M-SOP module. The objective function is updated to collaboratively maximize load recovery and smooth DG output as follows:

[0196]

[0197] While solving the above model, a strict extreme constraint on transient cooling load surge protection is imposed at a fine-grained time section, as expressed below:

[0198]

[0199] This results in a batch-staggered optimal recovery solution with surge protection safety guarantees.

[0200] Example 2:

[0201] To verify the effectiveness and impact of the method of this invention, this embodiment conducted the following experiments and data comparison analysis based on an improved 151-node and 295-node multi-voltage-level distribution network test system (including four voltage levels: 110kV, 35kV, 10kV, and 0.4kV):

[0202] 1. Experimental scenario and comparison scheme setup:

[0203] The distribution network is set to experience a line fault due to an extreme disaster (power outage duration set to 8 hours), and the proportion of temperature-controlled loads (TCLs) in the system is set to 60%. To highlight the advantages of this invention (considering multi-voltage level coordination, asymmetric M-SOP, and CLPU effects), the following four comparative schemes are set:

[0204] Option 1: Only medium-voltage network recovery, using symmetrical SOP, considering the CLPU effect;

[0205] Option 2: Coordinated recovery of medium and low voltage, using a symmetrical SOP, taking into account the CLPU effect;

[0206] Option 3: Coordinated recovery of medium and low voltage, using asymmetric M-SOP, without considering the CLPU effect (i.e., using a static load model).

[0207] Scheme 4 (the method of this invention): Medium and low voltage coordinated recovery, using asymmetric M-SOP, considering the CLPU effect.

[0208] 2. Data comparison and analysis:

[0209] 1. Verification of recovery efficiency and synergistic effect:

[0210] In the 151-node system, Scheme 1, relying solely on a medium-voltage symmetrical SOP, was limited by capacity bottlenecks and could only restore 95% of the load, taking 210 minutes. Scheme 2, by introducing low-voltage coordination, achieved 100% recovery, but because the symmetrical SOP could not flexibly match the surge current of the CLPU, the system could only passively wait for the surge to subside, taking as long as 148 minutes. In contrast, this invention, through the coordination of an asymmetrical M-SOP and a low-voltage SOP, can accurately deliver power to the heavily loaded area, achieving 100% load recovery in just 16 minutes while strictly adhering to CLPU transient constraints.

[0211] 2. Verification of physical safety and surge protection effectiveness:

[0212] While Scheme 3 can achieve 100% recovery in just 10 minutes, its neglect of the time-varying surge effect of CLPU (Constant Current Limiting Unit) could lead to catastrophic consequences in a real-world power grid. Experimental data shows that under Scheme 3, the voltage of many nodes drops to around 0.75 pu, far below the safety lower limit, and the power flow on multiple lines surges to 1.4 to 1.5 times the thermal stability limit due to inrush current. In contrast, the surge protection mechanism employed in this invention ensures that the voltage of all energized nodes remains robustly within the safe range of 0.95 pu-1.05 pu throughout the entire recovery scheduling cycle, and the power flow on all lines does not exceed the 1.0 pu thermal limit boundary, completely eliminating the risk of secondary power outages.

[0213] 3. Verification of the computational efficiency of the accelerated algorithm:

[0214] To address the curse of dimensionality caused by large-scale mixed-integer programming, this invention tested the proposed three-stage TS-RIPA acceleration algorithm. In a 151-node system, directly calling the commercial solver CPLEX to solve the original model took an average of 596.40 seconds, while using the TS-RIPA algorithm only took 44.69 seconds, achieving a computational speedup of more than 13.3 times while maintaining the accuracy of the solution.

[0215] In larger-scale 295-node systems, as integer variables grow exponentially, traditional CPLEX solvers fail to converge to a feasible solution within a 3600-second time limit (solution failure). However, the TS-RIPA algorithm proposed in this invention can still successfully output the globally optimal recovery strategy in an average of 171.06 seconds, which is not only much faster than the traditional two-stage acceleration algorithm (TSAA, requiring 427.59 seconds), but also demonstrates the superior computational efficiency and scalability of this invention in large-scale multi-voltage distribution network applications.

Claims

1. A dynamic load restoration method for multi-voltage level distribution networks considering time-varying cold load initiation, characterized in that, Includes the following steps: S1: Establish a time-varying cold load start-up model based on the lower triangular coefficient matrix to quantify the dynamic impact of outage duration and recovery time on load surges; S2: Construct a dynamic load recovery model for a multi-voltage-level distribution network, and comprehensively consider the constraints to form a mixed-integer second-order cone programming model with the main objective of maximizing the recovery load; S3: The three-stage relaxation-induction-polishing acceleration algorithm (TS-RIPA) is used to solve the mixed integer second-order cone programming model at a coarse-grained time scale to obtain the globally optimal coarse-grained mechanical topology sequence. S4: Map the mechanical topology sequence at the coarse-grained time scale to the fine-grained time scale using zero-order hold-up mapping. Under the condition of fixed topology, solve the pure time-series load high-frequency switching and equipment scheduling model, perform transient cold load surge protection verification, and output the final dynamic load recovery strategy.

2. The dynamic load restoration method for a multi-voltage distribution network considering time-varying cold load initiation as described in claim 1, characterized in that, The establishment of the time-varying cold load start-up model in step S1 includes: characterizing the time-varying load surge characteristics caused by the loss of diversity coefficients of the constant temperature control load after a long power outage through a lower triangular coefficient matrix, and constructing surge protection safety constraints.

3. The dynamic load restoration method for a multi-voltage distribution network considering time-varying cold load initiation according to claim 2, characterized in that, The process of establishing the time-varying cooling load start-up model in step S1 includes: The timing logic constraints are established as follows: ； ； ； Construct the lower triangular coefficient matrix The spatiotemporal dynamic evolution characteristics of cold load startup are described as follows: ； Among them, diagonal elements Indicates the corresponding power outage duration The initial surge peak multiplier; the first The column represents the corresponding subsequent load decay trajectory; The actual active and reactive power requirements of the nodes are calculated as follows: ； ； in, For discrete load recovery indicator variables, For a set of nodes, For time sets; to prevent voltage collapse caused by the superposition of surges during cold load startup, the surge protection safety constraints limiting the single-step load recovery amplitude are as follows: ； in, This is an indicator variable for load recovery actions.

4. The dynamic load restoration method for a multi-voltage distribution network considering time-varying cold load initiation as described in claim 3, characterized in that, The objective function of the multi-voltage level distribution network dynamic load recovery model in step S2 comprehensively considers maximizing the total restored load, minimizing distributed generation curtailment, minimizing main grid injected power, and minimizing network losses. The objective function is expressed as follows: ； The calculation formulas for each sub-objective are as follows: ； in, The target weight coefficient; For node load recovery state variables, The rated active load of the node; and These represent the available active power and actual output of the distributed power source, respectively. This contributes to the mainnet. This refers to internal losses within the standard operating procedure (SOP). The replacement variable is the square of the branch current. This is the branch resistance. To restore the total rated load, This is a reduction in active power for DG. Injecting positive energy into the mainnet and These are the internal losses of the SOP and the network line losses, respectively.

5. A dynamic load restoration method for a multi-voltage distribution network considering time-varying cold load initiation as described in claim 4, characterized in that, The constraints in step S2 include multi-voltage level distribution network topology reconfiguration constraints, multi-layer flexible interconnection equipment operation constraints, linearized DistFlow power flow constraints, and system operation safety constraints.

6. A dynamic load restoration method for a multi-voltage distribution network considering time-varying cold load initiation as described in claim 5, characterized in that, In step S2: The topology reconfiguration constraints for multi-voltage level distribution networks are constructed based on a virtual power flow model, as detailed below: The fault isolation constraints are as follows: ； The radial topology constraints of the multi-voltage level network are as follows: ； The constraints to prevent closed loops from forming between multiple SOP ports are as follows: ； The virtual power flow balance constraints are as follows: ； ； The constraint that virtual power flow is only allowed to flow in closed branches is as follows: ； In the formula, In branch connection state, The virtual root node status for the SOP port. As slack variables, For branch road virtual trend, It is a sufficiently large positive number; Operational constraints for multi-layer flexible interconnection devices include unified modeling of medium-voltage asymmetrical multiplexing intelligent soft switches and low-voltage symmetrical intelligent soft switches, as detailed below: The apparent power capacity uniform operating constraints are as follows: ； The active power conservation constraint considering internal conversion losses is as follows: ； For asymmetric M-SOP, the uniqueness allocation constraint of the VSC module is as follows: ； The dynamic capacity matching mapping constraints for M-SOP ports are as follows: ； In the formula, and Inject active and reactive power into the SOP port. For port capacity, The loss coefficient is... The binary selection matrix allocated to the VSC module. This refers to the module's rated capacity. Linearizing the DistFlow power flow constraint incorporates on-load tap-changing transformers and network losses into the calculation, as detailed below: The active power balance constraints at the nodes are as follows: ； Among them, transformer ratio parameters The definition is as follows: ； The reactive power balance constraints at the nodes are as follows: ； The voltage drop constraints for conventional circuits within the layer are as follows: ； The voltage drop constraint for a cross-voltage level transformer branch containing an OLTC is as follows: ； The OLTC discrete ratio adjustment constraints are as follows: ； In the formula, and For the active and reactive power flow of the line; The square of the node voltage magnitude; For OLTC discrete voltage turns ratio; For OLTC gear step size variables; System operational safety constraints include node voltage, branch thermal capacity, and distributed generation operating envelope boundary constraints, as detailed below: The node voltage magnitude constraints and root node voltage settings are as follows: ； The apparent power thermal limit constraint of the branch is as follows: ； The active power output constraints of distributed generation (DG) are as follows: ； The reactive power factor limits for distributed generation are as follows: ； The apparent power capacity limitations of distributed generation are as follows: 。 7. A dynamic load restoration method for a multi-voltage distribution network considering time-varying cold load initiation as described in claim 6, characterized in that, In step S3, a three-stage relaxation-induction-polishing acceleration algorithm is adopted. At a coarse-grained time scale, the constructed model is continuously relaxed, the auxiliary induced function is extracted as a pseudo gradient, and it is transformed into an auxiliary penalty term and added to the polishing objective function. The globally optimal coarse-grained mechanical topology sequence is obtained by solving the problem.

8. A dynamic load restoration method for a multi-voltage distribution network considering time-varying cold load initiation as described in claim 7, characterized in that, The execution process of the three-stage relaxation-induction-polishing acceleration algorithm in step S3 includes: A1: Topology relaxation: Reducing the time-series load scheduling variables Continuous relaxation, preserving mechanical topological variables The discrete properties of the object, with the objective of maximizing only the total restored active power load. Solving under the given conditions yields the globally optimal mechanical topology sequence. as follows: ； A2: Auxiliary induced function extraction: By fixing the mechanical topology constant, the load variables in the relaxed state are obtained by solving a continuous linear programming problem. The AIF factor, which serves as a pseudo-gradient, is extracted according to the following formula. : ； A3: Integer Polishing: Recovery The discrete integer properties of the AIF factor are used as an auxiliary penalty term to construct the polishing objective function, which quickly outputs a high-quality coarse-grained recovery sequence as follows: ； 。 9. A dynamic load restoration method for a multi-voltage distribution network considering time-varying cold load initiation as described in claim 8, characterized in that, Step S4 includes: B1: Zero-order time-scale-preserving mapping: mapping coarse-grained time domains Subdivided into fine-grained time-domain sets The determined mechanical topology is rigidly translated to a fine-grained time axis using zero-order hold logic as follows: ； B2: Fine-grained mixed-integer linear programming execution: Under a fixed mechanical topology, optimization is performed on the load switch operation and the dynamic capacity matching matrix of the M-SOP module. The objective function is updated to collaboratively maximize load recovery and smooth DG output as follows: ； While solving the above model, a strict extreme constraint on transient cooling load surge protection is imposed at a fine-grained time section, as expressed below: ； This results in a batch-staggered optimal recovery solution with surge protection safety guarantees.

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