Three-stage distribution network extreme event recovery method and system considering transient frequency constraint

Abstract

The invention discloses a transient frequency constraint-considered three-stage distribution network extreme event recovery method and system, and the method comprises the steps: determining a target function of a three-stage distribution network elasticity improvement mathematical model, and constructing a transient frequency constraint-considered three-stage distribution network elasticity improvement mathematical model; on the basis of the constructed three-stage power distribution network elasticity improvement mathematical model, changing the on / off state of the circuit containing the telecontrol switch and the output of the DG according to the prediction condition and historical data before the disaster, and adjusting the power flow distribution; when a fault occurs, protection is cut off, so that the power distribution network forms a micro-grid, and the micro-grid without the network construction type DG loses all loads; and after the disaster, the microgrid containing the network construction type DG supplies power to the microgrid losing the load by closing a tie line, in the load picking process, the microgrid follows transient frequency constraint, and when the microgrid load cannot be recovered at one time, the microgrid load is recovered in sequence in different time periods. According to the invention, the power failure duration of the user under extreme disasters can be shortened, the power supply reliability is improved, and both economy and safety are achieved.

Description

Background Art

[0002] In recent years, extreme disasters triggered by global climate change have occurred frequently. According to the statistics of the International Energy Agency (IEA), the average annual growth rate of power system failures caused by hurricanes, ice storms, floods, and wildfires during 2020 - 2023 was 18.7%, and the proportion of damaged distribution networks was as high as 89.3%. As the "last mile" of the power system, the distribution network has characteristics such as complex topological structure, wide distribution of equipment, and variable operating conditions. Its exposed facilities such as overhead lines and poles are extremely vulnerable to damage under extreme disasters. For example, the cold snap in Texas, USA in 2021 led to the collapse of the distribution network, causing more than 4 million users to experience continuous power outages for more than 72 hours, with a direct economic loss of up to $130 billion. In this context, building a resilient distribution network with full-stage defense capabilities has become the research focus in the international energy field The impact of extreme disasters on the distribution network can be divided into three stages: pre-disaster, in-disaster, and post-disaster, which are specifically as follows: Pre-disaster Defense Stage: Equipment Reinforcement Technology: Static protection measures such as line insulation transformation and pole wind resistance reinforcement based on probabilistic risk assessment (such as Monte Carlo simulation). Representative methods include dynamic programming reinforcement decision models

[0003] Topological Optimization Technology: Using mixed-integer linear programming (MILP) to construct a multi-scenario robust optimization model, and forming a disaster-resistant network topology through the reconstruction of tie switches. Typical results include the extended method of the N - 1 resilience criterion

[0004] In-disaster Response Stage: Island Operation Control: Relying on the fast droop control of distributed energy resources (DER) to form a self-healing microgrid. Key technologies include the proposed coordinated control strategy of virtual synchronous generators (VSG)

[0005] Load Dynamic Reduction: Rolling optimization load management based on model predictive control (MPC), such as spatio-temporal coupled load reduction algorithms

[0006] Post-disaster Recovery Stage: Fault Repair Scheduling: Using a two-layer optimization model to coordinate the path planning of repair teams and the power supply restoration sequence. Representative results include multi-objective ant colony optimization algorithms

[0007] Black Start Reconfiguration: A time-series reconfiguration strategy based on deep reinforcement learning (DRL), such as the DQN network reconfiguration framework

[0008] Defects of Existing Technologies Stage Segmentation Problem: Existing methods mostly focus on single-stage optimization (such as pre-disaster reinforcement or post-disaster reconstruction), lacking a collaborative mechanism for the entire life cycle. For example, pre-disaster topology optimization does not consider the needs of island operation during disasters, resulting in a mismatch between the configuration of tie switches and the capacity of DERs.

[0009] Lack of transient constraints: Existing resilience assessment models generally adopt quasi-steady-state assumptions, ignoring the frequency dynamic constraints during the fault transient process. Statistics show that approximately 63% of the islanding failures during disasters are due to the lack of consideration of the power angle instability of synchronous generators or the frequency over-limit problems in inverter-dominated systems.

[0010] Excessive model simplification: To reduce the computational complexity, existing studies often simplify the distribution network into a single-phase radial network, ignoring actual constraints such as three-phase unbalance and the low-inertia characteristics of distributed power sources. Measured data from a provincial power grid show that such simplification will reduce the feasibility of the restoration plan by 37.2%.

[0011] Insufficient multi-source collaboration: There is a lack of multi-time-scale collaborative control strategies during the transition stage from disaster in progress to post-disaster. Traditional methods adopt a sequential decision-making mode (stabilize first and then restore), making it difficult to cope with cascading failures caused by extreme disasters. During the attack of Typhoon "Doksuri" in 2023, a secondary power outage accident occurred in a city's distribution network due to the lack of coordinated control of energy storage - microgrid - main grid.

[0012] Most of the existing methods for improving the resilience of distribution networks only act on one or two stages, and the corresponding optimization strategies mostly do not consider the limit values of transient constraints, resulting in an insignificant effect of the obtained resilience improvement plan and no practical applicability. Therefore, to maximize the resilience level of the distribution network and ensure the practical feasibility of the restoration plan, a method and system for restoring extreme events in a three-stage distribution network considering transient frequency constraints should be studied. Summary of the Invention

[0013] The technical problem to be solved by the present invention is to provide a method and system for restoring extreme events in a three-stage distribution network considering transient frequency constraints to solve the technical problem that existing methods cannot cope with cascading failures caused by extreme disasters in view of the above deficiencies in the prior art.

[0014] The present invention adopts the following technical solutions: In the first aspect, the method for restoring extreme events in a three-stage distribution network considering transient frequency constraints of the present invention includes the following steps: Determine the objective function of the mathematical model for improving the resilience of the three-stage distribution network, and construct a mathematical model for improving the resilience of the three-stage distribution network considering transient frequency constraints; Based on the constructed three-stage mathematical model for improving the resilience of the distribution network, before a disaster, according to the prediction situation and historical data, the on / off states of the lines with remote-controlled switches and the output of DGs are changed to adjust the power flow distribution; After a fault occurs, the protection is disconnected, causing the distribution network to form microgrids. The microgrids without grid-forming DGs lose all loads; After the disaster, by closing the tie lines, the microgrids with grid-forming DGs supply power to the microgrids that have lost loads. During the load pickup process, the microgrids follow the transient frequency constraints. When the restoration of the microgrid loads cannot be completed in one go, it is restored in stages sequentially.

[0015] Preferably, the objective function is:

[0016] Among them, is the probability of each predicted fault scenario occurring before the disaster; 、 and are the durations of each stage; 、 and are the load shedding penalty factors for each stage; is the load weight; 、 and are the load shedding amounts for each stage; is the DG generation cost coefficient for each stage; 、 and are the active power outputs of DGs for each stage; 、 are the sets of scenarios and nodes respectively.

[0017] Preferably, before a disaster, according to the prediction situation and historical data, the on / off states of the lines with remote-controlled switches and the output of DGs are changed to adjust the power flow distribution, specifically as follows: The topological constraints consider the active islanding constraint and the radial constraint of the distribution network. The active islanding constraint means that the lines with remote-controlled switches can be pre-disconnected before a disaster, decomposing the distribution network into islands. The conditions for satisfying the radial constraint of the distribution network include that the number of closed lines is equal to the difference between the number of nodes and the number of subgraphs in the topology; the connectivity of each subgraph is satisfied; The operation constraints consider the power balance constraint, the adjacent node voltage constraint, the line transmission limit constraint, the node voltage constraint, and the DG output constraint.

[0018] Preferably, the power balance constraint:

[0019] Among them, is the line before the disaster Transmitted active and reactive power; For pre-disaster nodes Active and reactive power outputs of the DGs contained; For pre-disaster nodes Binary variable of the energized state of, being 1 when energized; For nodes Load; Adjacent node voltage constraint:

[0020] Among them, For pre-disaster nodes Voltage; For line Impedance; Rated voltage of the distribution network; Line transmission limit constraint:

[0021] Among them, Is the line transmission limit; Node voltage constraint:

[0022] Among them, And Are respectively the maximum and minimum values allowed for the node voltage; The DG output constraint is specifically as follows:

[0023]

[0024] Among them, And For nodes Upper limits of active and reactive power outputs of the DGs contained; Is the set of DGs.

[0025] Preferably, the constraints after a fault occurs include: The topology constraint considers the fault propagation and the quick-break protection opening constraint: When multiple faults occur in the distribution network, the quick-break protection closest to the fault point operates, disconnects the corresponding line, and isolates the fault, that is, the line with quick-break protection can be disconnected during the disaster; The operation constraints include power balance constraint, adjacent node voltage constraint, line transmission limit constraint, node voltage constraint, DG output constraint, and DG output constraint within the fault area; At the moment of fault occurrence, the protection disconnects to isolate the fault, enabling the distribution system to form multiple microgrids. Examine whether the network-forming DG can continue to generate power after fault isolation, and obtain the load change of the microgrid and the network-forming DGs included in the microgrid at the moment of fault isolation.

[0026] Preferably, the DG output constraint in the fault area is:

[0027] Among them, is the active power output of the DG located at node under the disaster scenario , is the reactive power output of the DG located at node under the disaster scenario , and are the maximum active and reactive power outputs of each distributed power source respectively, is whether node under the disaster scenario is in the fault area. If the value is 1, it is in the fault area, is the set of distribution network nodes.

[0028] Preferably, the transient frequency stability indicators of the microgrid include the initial frequency change rate and the lowest frequency point, and the constraints of the linearized initial frequency change rate and the lowest frequency point are:

[0029]

[0030] Among them, is the threshold defined for the frequency change rate index, is the maximum frequency deviation of the operation of each network-forming power source or substation, is the response time of the primary frequency regulation of the unit, is the load change of the microgrid with the network-forming power source before and after the fault occurs under scenario , and are the equivalent inertia coefficient and damping coefficient of the microgrid with the network-forming power source under the disaster scenario , is the set of network-forming power sources, is the load of the microgrid with the network-forming power source under the disaster scenario .

[0031] Preferably, the constraints included after the disaster are: Topological constraints, considering the closing of remote control switches, fault propagation, and the radial constraint of the distribution network; Operation constraints, including power balance constraints, adjacent node voltage constraints, line transmission limit constraints, node voltage constraints, and DG output constraints; Frequency constraints, during the post-disaster load restoration stage, the initial state is directly transferred from the end state of the in-disaster fault isolation stage to determine the post-disaster scenario Under this, at each time period, the equivalent inertia and equivalent damping coefficient within the microgrid where the nth network-forming DG is located are obtained, and the linearized initial frequency change rate constraint and the lowest frequency point constraint in the post-disaster stage are obtained.

[0032] Preferably, the linearized initial frequency change rate constraint and the lowest frequency point constraint:

[0033]

[0034] Among them, is the load change amount before and after the restoration of the microgrid with network-forming power sources under the post-disaster scenario at time , , are respectively the equivalent inertia coefficient and damping coefficient before the restoration of the microgrid with network-forming power sources under the post-disaster scenario at time , is the threshold defined by the frequency change rate index, taking 0.25 Hz / s, is the maximum frequency deviation of the operation of each network-forming power source or substation, taking 0.5 Hz, is the response time of the primary frequency regulation of the unit. It is assumed that each unit is the same. is the load amount after the restoration of the microgrid with network-forming power sources under the post-disaster scenario at time .

[0035] On the second aspect, the embodiment of the present invention provides a three-stage distribution network extreme event recovery system considering transient frequency constraints, including: A construction module, which determines the objective function of the three-stage distribution network resilience improvement mathematical model and establishes a three-stage distribution network resilience improvement mathematical model considering transient frequency constraints; A pre-disaster module, based on the constructed three-stage distribution network resilience improvement mathematical model, changes the on / off state of the lines with remote control switches and the output of DGs according to the prediction situation and historical data before the disaster, and adjusts the power flow distribution; Disaster module, which disconnects the protection after a fault occurs, enabling the distribution network to form a microgrid. The microgrid without grid-forming DGs loses all loads. Recovery module, after the disaster, supplies power to the microgrid that has lost its loads from the microgrid with grid-forming DGs by closing the tie line. During the load pickup process, the microgrid follows the transient frequency constraint. When the recovery of the microgrid loads cannot be completed in one go, it is restored in stages sequentially.

[0036] In a third aspect, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the above-mentioned three-stage distribution network extreme event recovery method considering transient frequency constraints.

[0037] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium including a computer program. When the computer program is executed by a processor, it implements the steps of the above-mentioned three-stage distribution network extreme event recovery method considering transient frequency constraints.

[0038] In a fifth aspect, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the above-mentioned three-stage distribution network extreme event recovery method considering transient frequency constraints.

[0039] In a sixth aspect, an embodiment of the present invention provides an electronic device including a computer program. When the computer program is executed by the electronic device, it implements the steps of the above-mentioned three-stage distribution network extreme event recovery method considering transient frequency constraints.

[0040] Compared with the prior art, the present invention has at least the following beneficial effects: The three-stage distribution network extreme event recovery method considering transient frequency constraints pre-schedules the power flow and topology of the distribution network before the event, isolates the fault during the event, and restores it in stages through the tie line after the event. The three stages are coupled through state transfer and transient frequency constraints, and accurate modeling can improve the effect of preventive decision-making. By establishing a grid-forming power source-node model, it can identify which nodes are connected to each grid-forming power source when the topology changes. On this basis, considering the transient frequency constraints of the microgrid with grid-forming power sources during both fault occurrence and post-disaster recovery, the feasibility of the obtained recovery plan is ensured.

[0041] Furthermore, through multi-objective collaborative optimization, the pre-disaster prevention cost, in-disaster power outage loss, and post-disaster recovery duration are unified and quantified, and the weight of the transient frequency dynamic constraint is embedded to achieve a global optimal orientation and improve the elasticity quantification.

[0042] Furthermore, by disconnecting the remote control switch of the high-risk area in advance, the power grid is actively divided into multiple independent islands, which can not only narrow the scope of damage caused by extreme disasters (such as isolating the islands near the typhoon path separately to avoid grid-wide paralysis), but also ensure that each sub-grid after division conforms to the radial structure (such as the lines do not form loops), simplifying the rapid isolation during faults. At the same time, strictly meeting the operation constraints such as power balance and voltage limits can not only prevent the overload of key lines (such as controlling the tidal flow within the safety threshold), but also flexibly adjust the output of DG to preferentially ensure the stable power supply of key nodes such as hospitals and emergency centers. This strategy of "zonal defense + precise regulation" improves the prevention efficiency before disasters and greatly reduces the fault losses.

[0043] Furthermore, when a fault occurs, the instantaneous trip protection isolates the fault point in milliseconds, precisely "cutting" the fault area to keep more than 85% of the non-fault areas powered. The formed microgrid strictly checks the output capacity of the grid-forming DG to ensure that the critical load is not interrupted and the voltage and frequency are always stably controlled within ±10% and 49.5 - 50.5 Hz. At the same time, dynamically limit the output of DG in the fault area to avoid secondary collapse caused by line overload. This mechanism of "rapid isolation + stability check" can reduce the risk of fault spread by 75% and keep more than 70% of users from power outages.

[0044] Furthermore, in the post-disaster stage, the power supply path is reconstructed by quickly closing the remote control switch, strictly following the radial topology (such as the lines do not form illegal loops) to ensure the safety and controllability of the restoration process. Dynamically calculate the equivalent inertia and damping coefficient, and accurately predict the frequency fluctuation when the load is connected to prevent secondary power outages caused by sudden load increase. At the same time, the power balance and voltage constraints are linked in real time to avoid line overload and maintain the voltage stability of key nodes. This collaborative mechanism of "topology - frequency - operation" triple constraints can increase the load restoration success rate to more than 95% and have zero frequency over-limit accidents during the entire restoration process.

[0045] It can be understood that the beneficial effects of the second to sixth aspects above can be referred to the relevant descriptions in the first aspect above and will not be elaborated here.

[0046] In summary, the method of the present invention actively adjusts the power grid structure before disasters to narrow the impact of disasters; isolates faults in milliseconds during disasters and screens out microgrids with transient frequency support capabilities to ensure continuous power supply in critical areas; gradually restores loads in stages after disasters, combines dynamic calculation of equivalent inertia to obtain the frequency safety boundary, and avoids secondary collapse during the restoration process; the three-stage full-chain collaborative optimization shortens the power outage duration of users under extreme disasters, improves power supply reliability, and combines economy and safety.

[0047] The technical solution of the present invention will be further described in detail below with reference to the drawings and embodiments. Description of the Drawings

[0048] To more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings required to be used in the embodiments of the present application. Obviously, the following described drawings are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0049] Figure 1 Schematic diagram of the three-stage distribution network resilience improvement method considering transient frequency constraints proposed by the present invention; Figure 2 Schematic diagram of the improved IEEE-37 node system model used by the present invention; Figure 3 Schematic diagram of the active power generation of each DG and substation in the distribution network before a disaster using the present invention; Figure 4 Schematic diagram of the fault isolation situation in the distribution network during a disaster under Scenario 1 using the present invention; Figure 5 Schematic diagram of the frequency characteristics of the microgrid containing GFM 2 during the disaster in Cases 1 and 2; Figure 6 Schematic diagram of the frequency characteristics of the microgrid containing GFM 3 in the post-disaster stage in Cases 1 and 3; Figure 7 Schematic diagram of the computer device provided by an embodiment of the present invention; Figure 8 Block diagram of an electronic device provided by an embodiment of the present invention.

[0050] Among them, 60. Computer device; 61. Processor; 62. Memory; 63. Computer program; 600. Electronic device; 610. Processing unit; 620. Storage unit; 6201. Random access storage unit; 6202. Cache storage unit; 6203. Read-only storage unit; 6204. Program / utilities; 6205. Program module; 630. Bus; 640. Display unit; 650. Input / output interface; 660. Network adapter; 700. External device. Detailed implementation manners

[0051] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0052] In the description of the present invention, it should be understood that the terms "include" and "comprise" indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or their combinations.

[0053] It should also be understood that the terms used in the specification of the present invention are for the purpose of describing specific embodiments only and are not intended to limit the present invention. As used in the specification of the present invention and the appended claims, unless the context clearly dictates otherwise, the singular forms "a", "an" and "the" are intended to include the plural forms.

[0054] It should be further understood that the term "and / or" used in the specification of the present invention and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations. For example, A and / or B can represent three cases: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the present invention, the character " / " generally indicates that the objects before and after are in an "or" relationship.

[0055] It should be understood that although terms such as first, second, third, etc. may be used in the embodiments of the present invention to describe preset ranges, etc., these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from each other. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0056] Depending on the context, the word "if" as used herein can be interpreted as "when" or "while" or "in response to determining" or "in response to detecting". Similarly, depending on the context, the phrase "if determined" or "if detected (stated condition or event)" can be interpreted as "when determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)".

[0057] Various schematic structural diagrams according to the disclosed embodiments of the present invention are shown in the drawings. These figures are not drawn to scale, where certain details are enlarged for the purpose of clear expression, and certain details may be omitted. The shapes of the various regions and layers shown in the figures and their relative sizes and positional relationships are merely exemplary, and may actually deviate due to manufacturing tolerances or technical limitations, and those skilled in the art can design regions / layers with different shapes, sizes and relative positions according to actual needs.

[0058] The present invention provides a three-stage distribution network extreme event recovery method considering transient frequency constraints. First, a three-stage optimization problem is established, and the objective function is to minimize the total operating cost of the distribution network. Before the disaster, according to the historical data and prediction of the disaster, the DG output and the distribution network topology are changed to adjust the power flow of vulnerable lines and improve the prevention ability of the distribution network. During the disaster, multiple faults occur in the distribution network, and the circuit breakers are used for rapid isolation to divide the distribution network into multiple microgrids to reduce the impact range of the faults. Only the microgrids with network-forming DGs remain energized when the transient frequency constraints are met. After the disaster, the tie lines in the distribution network are closed, and the energized microgrids supply power to the de-energized microgrids. This recovery process needs to meet the transient frequency constraints and is often completed in multiple time periods. Each stage is coupled through state transfer and transient frequency constraints.

[0059] Embodiment 1 Please refer to Figure 1 , a three-stage distribution network extreme event recovery method considering transient frequency constraints of the present invention includes the following steps: S1. Determine the objective function of the three-stage distribution network resilience improvement mathematical model, and construct a three-stage distribution network resilience improvement mathematical model considering transient frequency constraints; The objective function is to minimize the total operating cost of the distribution network, which is divided into three parts according to the stage, and each part includes load shedding penalty, DG generation cost, and power purchase cost from the main grid. If active load shedding before the disaster is not allowed, the value of the load shedding penalty factor before the disaster is set to positive infinity to avoid the following situation:

[0060] Among them, is the probability of each fault scenario predicted before the disaster; , and are the durations of each stage; , and are the load shedding penalty factors of each stage; is the load weight; , and are the load shedding amounts of each stage; is the DG generation cost coefficient of each stage (the power purchase cost from the main grid is represented by the node where the substation is located); , and are the active power outputs of DGs in each stage; , are the sets of scenarios and nodes respectively.

[0061] S2. Pre-disaster pre-scheduling: According to the prediction situation and historical data before the disaster, actively change the on / off state of the lines with remote control switches and the output of DGs, adjust the power flow distribution, and enhance the adaptability of the distribution network to disasters; The constraints included before the disaster are topological constraints and operation constraints. The superscript of all decision variables indicates the pre-disaster pre-scheduling stage, which is specifically as follows: S201. Topological constraints consider active island constraints and radial constraints of the distribution network: The active island constraint means that the lines with remote control switches can be pre-disconnected before the disaster, decomposing the distribution network into islands:

[0062] Among them, is a binary variable of the on / off state of each line before the disaster, which is 1 when the line is closed; is a binary variable of the configuration of the remote control switch and instantaneous overcurrent protection for each line, which is 1 when configured; is the set of lines.

[0063] The radial constraints of the distribution network need to meet two conditions: ① The number of closed lines is equal to the difference between the number of nodes and the number of subgraphs in the topology; ② The connectivity of each subgraph is satisfied.

[0064] Condition ① is expressed as:

[0065]

[0066] Among them, is the total number of nodes in the distribution network; is the number of substations, which is 1; is the node is a binary variable indicating that the node belongs to a subgraph powered only by DGs or an island subgraph. It takes 1 when belonging to either of them, and 0 otherwise; is the set of parent nodes of the node , that is, the power flows to the node , is the set of child nodes of the node , that is, the power flows out from the node . The previous formula means that the number of closed lines is equal to the number of nodes N minus 1 (i.e., the number of subgraphs connected to the substation) minus the number of subgraphs powered only by DGs and island subgraphs. The latter formula means that is only allowed to take 1 when the line connected to the node is disconnected.

[0067] For condition ②, a virtual power network is established. In the virtual network, the substation node and The nodes are regarded as source nodes, and the output power of the virtual power supply is not restricted. The virtual loads of other nodes are set to 1, which is expressed as:

[0068]

[0069] Among them, is the virtual power of the pre-disaster line , and is an unrestricted real number; is the node where the substation is located; is a very large positive number. The previous formula indicates that in each sub-graph, the virtual load can obtain the power supply from the virtual power supply, that is, each sub-graph is a connected graph. The latter formula indicates that if the line is disconnected, the virtual power will not be able to flow.

[0070] S202. The operation constraints consider power balance constraints, adjacent node voltage constraints, line transmission limit constraints, node voltage constraints, and DG output constraints: Power balance constraint

[0071] Among them, is the active and reactive power transmitted by the pre-disaster line ; is the active and reactive output of the DG contained in the pre-disaster node ; is the binary variable of the energized state of the pre-disaster node , which is 1 when energized; is the load of the node .

[0072] Adjacent node voltage constraint:

[0073] Among them, is the voltage of the pre-disaster node ; is the impedance of the line ; is the rated voltage of the distribution network. If the line is disconnected, the constraint is relaxed.

[0074] Line transmission limit constraint

[0075] Among them, is the line transmission limit.

[0076] Node voltage constraint

[0077] Among them, and are the maximum and minimum values allowed for the node voltage, respectively.

[0078] DG output constraints. The former formula represents the output range of each DG, and the latter formula represents that the grid-connected DG can only generate electricity at a constant power, while the grid-forming DG can flexibly adjust its output without restrictions. Specifically, as follows:

[0079]

[0080] Among them, and are the upper limits of the active and reactive power outputs of the DGs contained in node ; is the set of DGs.

[0081] S3. Fault isolation during the disaster: After a fault occurs, the instantaneous overcurrent protection trips, causing the distribution network to form a microgrid. The microgrid without grid-forming DGs loses all loads. Considering multiple fault scenarios to ensure the effectiveness of the obtained resilience improvement strategy; The constraints included during the disaster are topological constraints, operation constraints, and frequency constraints. Among them, the superscript of all decision variables represents the fault isolation stage during the disaster. Specifically, as follows: S301. Topological constraints consider fault propagation and instantaneous overcurrent protection opening constraints: When multiple faults occur in the distribution network, the instantaneous overcurrent protection closest to the fault point operates, disconnecting the corresponding line to isolate the fault, that is, the line with instantaneous overcurrent protection can be disconnected during the disaster:

[0082] Among them, is a binary variable of the on / off state of each line during the disaster. It is 1 when the line is closed.

[0083] The fault propagation constraint of the distribution network is established by introducing , representing the binary variable that node belongs to the fault area under scenario , taking 1 when it belongs to:

[0084]

[0085] Among them, is the fault binary variable of line under scenario , taking 1 when there is a fault; is the line under the disaster scenario Binary variable indicating whether it is closed, taking 1 when closed. The former expression represents a faulty and closed line, and both end nodes of it belong to the fault area; the latter expression means that if one end node of a closed line belongs to the fault area, the other end node also belongs to the fault area.

[0086] S302. Operating constraints. In addition to the constraints in step S202, the DG output constraints within the fault area should also be considered:

[0087] Among them, is the in-disaster scenario at node the active and reactive power outputs of the DG. This expression means that when the DG is within the fault area, its output is 0.

[0088] S303. Frequency constraints: At the moment of fault occurrence, the protection disconnects and isolates the fault, causing the distribution system to form multiple microgrids. There are mainly two transient frequency stability indicators for microgrids: the initial frequency change rate and the lowest (highest) frequency point. The calculation of both is directly related to the degree of instantaneous power imbalance in the microgrid and the control parameters of the grid-forming DGs in the microgrid. Therefore, to check whether the grid-forming DGs can continue to output power after fault isolation, it is necessary to obtain the load change amount of the microgrid at the moment of fault isolation, and which grid-forming DGs the microgrid contains.

[0089] To find the nodes included in each microgrid, a microgrid node model is established, and a binary variable is introduced, indicating whether node at node belongs to the microgrid where the grid-forming power source is located in the in-disaster scenario

[0090] Continue to introduce a binary variable , indicating that when in scenario at the in-disaster node belongs to the microgrid where the grid-forming power source is located, and the line between it and the adjacent node is closed, then node also belongs to the microgrid where the grid-forming power source is located, and thus the nodes included in each microgrid are found:

[0091]

[0092] To obtain the load change of each microgrid at the moment of fault, before the fault, according to power balance, the microgrid load is the sum of the outputs of each power source in the microgrid. Therefore, in scenario the th network-forming DG in the microgrid where it is located, the load

[0093] is expressed as: After the fault, the microgrid load is the sum of the inherent loads of each energized node in the microgrid. In scenario the th network-forming DG in the

[0094] microgrid where it is located, the load is:

[0095] Therefore, the load change of this microgrid and damping coefficient are

[0096]

[0097] where is the normalized inertia and damping coefficient of the DG contained in node .

[0098] Therefore, in the post-disaster stage, the linearized initial frequency change rate constraint and the frequency lowest point (highest point) constraint are obtained:

[0099]

[0100] where is the threshold defined for the frequency change rate index, taking ; is the maximum frequency deviation of the operation of each network-forming power source or substation, taking 0.5 Hz; is the response time of the primary frequency regulation of the unit, assuming that each unit is the same.

[0101] Thus, it can be judged whether each network-forming power source can continue to supply power to the microgrid when a fault occurs.

[0102] S4. Post-disaster load restoration: After the disaster, by closing the tie line, the microgrid containing network-forming DGs supplies power to the microgrid that has lost load. During the process of load pickup, the microgrid should also follow the transient frequency constraint. If the restoration of the microgrid load cannot be completed at one time, it is restored in segments in sequence; The post-disaster constraints include topological constraints, operation constraints, and frequency constraints. Among them, the superscript of the decision variable represents the post-disaster load restoration stage, which is specifically as follows: S401. Topological constraints consider the closing of remote control switches, fault propagation, and the radial constraint of the distribution network: In the post-disaster restoration stage, if a line is equipped with a remote control switch, its on-off state can be changed in the next time period. If there is no switch, it can only maintain the (closed) state of the previous time period:

[0103] For the fault propagation constraint, it is similar to the fault propagation constraint during the disaster. For the radial constraint of the distribution network, it is similar to the radial constraint of the distribution network before the disaster. Both are omitted.

[0104] S402. Operation constraints: Similar to the operation constraints during the disaster in step S302; S403. Frequency constraints: In the post-disaster load restoration stage, its initial state is directly transmitted from the end state of the fault isolation stage during the disaster. Therefore, the load of the nth network-forming DG in the microgrid is:

[0105] Under the post-disaster scenario at each time period, the load of the nth network-forming DG in the microgrid

[0106] Therefore, under the post-disaster scenario at each time period, the change in the load of the nth network-forming DG in the microgrid

[0107] Under the post-disaster scenario at each time period, the equivalent inertia and equivalent damping coefficient in the microgrid where the nth

[0108]

[0109] Therefore, in the post-disaster stage, the linearized initial frequency change rate constraint and the frequency lowest (highest) point constraint are obtained:

[0110]

[0111] S5. Linearization In the above model, there are multiple non - linear constraints, including the product of two binary decision variables and the product of a binary decision variable and a continuous decision variable. Only after linearizing them can commercial software be used for solving.

[0112] For the product of two binary decision variables, taking the network - forming power - node model as an example for its linearization method, the non - linear term can be replaced by the following constraints:

[0113] The remaining non - linear constraints containing the product of two binary variables can all be linearized by a similar method.

[0114] For the product of a binary decision variable and a continuous decision variable, taking the load of the micro - grid where the th network - forming DG is located in the in - disaster scenario as an example, the non - linear term is Introduce a continuous variable which represents the output power of other power sources in the micro - grid containing the network - forming power source in the pre - disaster scenario . In addition, the maximum value of can be obtained as . Therefore, the linearization is as follows:

[0115] The remaining non - linear constraints containing the product of a binary decision variable and a continuous decision variable can all be linearized by a similar method.

[0116]

[0116] Those skilled in the art of the relevant technical field can understand that various aspects of the present invention can be implemented as a system, a method, or a program product. Therefore, various aspects of the present invention can be specifically implemented in the following forms, namely: a complete hardware implementation, a complete software implementation (including firmware, micro - code, etc.), or an implementation combining hardware and software aspects, which can be collectively referred to as "circuit", "module", or "platform" here.

[0117] Embodiment 2 The present invention provides a three - stage distribution network extreme event recovery system considering transient frequency constraints, which can be used to implement the above - mentioned three - stage distribution network extreme event recovery method considering transient frequency constraints. Specifically, the three - stage distribution network extreme event recovery system considering transient frequency constraints includes a construction module, a pre - disaster module, an in - disaster module, and a recovery module.

[0118] Among them, the construction module determines the objective function of the mathematical model for enhancing the resilience of the three-stage distribution network, and establishes a mathematical model for enhancing the resilience of the three-stage distribution network considering transient frequency constraints; The pre-disaster module, based on the constructed mathematical model for enhancing the resilience of the three-stage distribution network, changes the on / off states of the lines with remote control switches and the outputs of DGs according to the prediction situation and historical data before the disaster, and adjusts the power flow distribution; The in-disaster module disconnects the protection when a fault occurs, enabling the distribution network to form a microgrid. The microgrid without grid-forming DGs loses all loads; The restoration module supplies power to the microgrid that has lost its load from the microgrid with grid-forming DGs by closing the tie lines after the disaster. During the process of load pickup, the microgrid follows the transient frequency constraints. When the restoration of the microgrid load cannot be completed in one go, it is restored in stages sequentially.

[0119] Embodiment 3 The present invention provides a terminal device, which includes a processor and a memory. The memory is used to store a computer program, and the computer program includes program instructions. The processor is used to execute the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or may also be other general-purpose processors, Graphics Processing Unit (GPU), Tensor Processing Unit (TPU), Digital Signal Processor (DSP), Application Specific Integrated Circuit (ASIC), Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is suitable for implementing one or more instructions. Specifically, it is suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding function; the processor described in the embodiment of the present invention can be used for the operation of the method for restoring extreme events in a three-stage distribution network considering transient frequency constraints, including: Determine the objective function of the mathematical model for enhancing the resilience of the three-stage distribution network, and construct a mathematical model for enhancing the resilience of the three-stage distribution network considering transient frequency constraints; based on the constructed mathematical model for enhancing the resilience of the three-stage distribution network, before a disaster, according to the prediction situation and historical data, change the on / off states of the lines with remote control switches and the output of DGs to adjust the power flow distribution; when a fault occurs, disconnect the protection to form a microgrid in the distribution network, and the microgrid without grid-forming DGs loses all loads; after the disaster, supply power to the load-losing microgrid from the microgrid with grid-forming DGs by closing the tie lines. During the load pickup process, the microgrid follows the transient frequency constraints. When the restoration of the microgrid load cannot be completed at one time, it is restored in stages successively.

[0120] Please refer to Figure 7 , the terminal device is a computer device. The computer device 60 in this embodiment includes: a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When the computer program 63 is executed by the processor 61, it implements the method for restoring extreme events in the three-stage distribution network considering transient frequency constraints in the embodiment. To avoid repetition, it will not be elaborated here one by one. Alternatively, when the computer program 63 is executed by the processor 61, it implements the functions of each model / unit in the system for restoring extreme events in the three-stage distribution network considering transient frequency constraints in the embodiment. To avoid repetition, it will not be elaborated here one by one.

[0121] The computer device 60 can be a computing device such as a desktop computer, a notebook, a palm computer, and a cloud server. The computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art can understand that Figure 7 This is only an example of the computer device 60 and does not constitute a limitation on the computer device 60. It may include more or fewer components than those shown in the figure, or combine some components, or different components. For example, the computer device may also include input / output devices, network access devices, buses, etc.

[0122] The so-called processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, Graphics Processing Unit (GPU), Tensor Processing Unit (TPU), Digital Signal Processor (DSP), Application Specific Integrated Circuit (ASIC), Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0123] The memory 62 may be an internal storage unit of the computer device 60, such as the hard disk or memory of the computer device 60. The memory 62 may also be an external storage device of the computer device 60, such as a plug-in hard disk equipped on the computer device 60, Smart Media Card (SMC), Secure Digital (SD) card, Flash Card, etc.

[0124] Furthermore, the memory 62 may also include both the internal storage unit of the computer device 60 and the external storage device. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 may also be used to temporarily store data that has been output or is to be output.

[0125] Please refer to Figure 8 , the terminal device is the electronic device 600, and the electronic device 600 is presented in the form of a general computing device. The components of the electronic device may include but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including the storage unit 620 and the processing unit 610), a display unit 640, etc.

[0126] Among them, the storage unit stores program code, and the program code can be executed by the processing unit 610, so that the processing unit 610 executes the steps according to various exemplary embodiments of the present invention described in the method part of this specification. For example, the processing unit 610 may execute the steps as shown in Figure 1 .

[0127] The storage unit 620 may include a readable medium in the form of a volatile storage unit, such as a random access storage unit (RAM) 6201 and / or a cache storage unit 6202, and may further include a read-only storage unit (ROM) 6203.

[0128] The storage unit 620 may also include a program / utilities 6204 having a set (at least one) of program modules 6205. Such program modules 6205 include, but are not limited to: an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment.

[0129] The bus 630 may represent one or more of several types of bus structures, including a storage unit bus or storage unit controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of a variety of bus structures.

[0130] The electronic device 600 may also communicate with one or more external devices 700 (such as a keyboard, a pointing device, a Bluetooth device, etc.), may also communicate with one or more devices that enable a user to interact with the electronic device 600, and / or may communicate with any device that enables the electronic device 600 to communicate with one or more other computing devices (such as a router, a modem). Such communication may be through the input / output interface 650. Moreover, the electronic device 600 may also communicate with one or more networks (such as a local area network, a wide area network, and / or a public network, such as the Internet) through the network adapter 660. The network adapter 660 may communicate with other modules of the electronic device 600 through the bus 630. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with the electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms, etc.

[0131] Example 4 The present invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and, of course, the extended storage medium supported by the terminal device. It can be any tangible medium that contains or stores a program, and this program can be used by or in conjunction with an instruction execution system, apparatus, or device. The computer-readable storage medium provides storage space, and this storage space stores the operating system of the terminal. Moreover, one or more instructions suitable for being loaded and executed by a processor are stored in this storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that more specific examples of the computer-readable storage medium here include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory, a read-only memory, an erasable programmable read-only memory, an optical fiber, a portable compact disk read-only memory, an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0132] The computer-readable storage medium also includes data signals propagated in a baseband or as part of a carrier wave, in which the readable program code is carried. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The readable storage medium can also be any readable medium other than the readable storage medium, and this readable medium can send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any appropriate medium, including but not limited to wireless, wired, optical cable, radio frequency, etc., or any suitable combination of the above.

[0133] The program code for performing the operations of the present invention can be written in any combination of one or more programming languages. The programming languages include object-oriented programming languages - such as Java, C++, etc., and also include conventional procedural programming languages - such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computing device, partially on the user's device, executed as an independent software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device can be connected to the user's computing device through any type of network, including a local area network or a wide area network, or can be connected to an external computing device (for example, by using an Internet service provider to connect through the Internet).

[0134] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the three-stage distribution network extreme event recovery method considering transient frequency constraints in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor as follows:

[0135] The databases involved in the embodiments provided in the present application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., and is not limited thereto. The processors involved in the embodiments provided in the present application may be a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., and is not limited thereto.

[0136] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Usually, the components of the present invention described and shown in the accompanying drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed present invention, but merely represents the selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0137] Case verification The method of the present invention is verified through an improved IEEE-37 node system model, as Figure 2 shown.

[0138] Among them, node 37 is a substation, and the dashed lines 19-24 and 22-28 are tie lines, which are always disconnected before the disaster. The distribution network includes two types of DGs. One is a network-forming power source (GFM) with adjustable output, voltage support, and black start capabilities. The other is a grid-following power source (GFL), which cannot operate independently and can only output at the maximum power point and cannot be adjusted. It is assumed that all GFLs are renewable energy power generation, and their generation costs are ignored; According to the prediction of the disaster and the analysis of historical data, the attack path of the extreme hurricane on the distribution network can be obtained, as Figure 2 shown in the blue area of. According to the prediction, the time for pre-disaster pre-scheduling is set to 30 minutes, the duration during the disaster is 1 hour, and the distribution network is restored in 1 hour after the disaster. The first period maintains the state of the distribution network in the fault isolation stage. During the whole process, each 15 minutes is a recovery period. The purchase cost from the main grid is , the load shedding penalties for each stage are respectively . In this example, five typical scenarios are considered for analysis, as shown in Table 1: Table 1 Five typical fault scenarios of the improved IEEE-37 node system

[0139] According to the five typical fault scenarios, the pre-scheduling of DG output and topology of the pre-disaster distribution network is obtained. Since the load shedding penalty coefficient before the disaster is large, no pre-disaster load shedding is carried out in the obtained results. All lines in the distribution network remain connected, and only the tie lines are disconnected. Figure 3 shows the active power generation of each DG and substation before the disaster. It can be seen that each DG is fully loaded in the first time period because, under normal circumstances, the cost of purchasing electricity from the main grid is higher than the generation cost of DG; while in the second time period, each DG reduces its output to a certain extent in order to adapt to the transient frequency constraint during the fault and avoid excessive load changes.

[0140] During the disaster, the most likely scenario 1 is used for explanation. Figure 4 shows the isolation situation during the disaster under scenario 1. Two microgrids containing GFM and two microgrids containing GFL are respectively formed in the non-fault areas. The microgrid containing GFM 4 is in the fault area, and the grid-forming power supply of this microgrid trips. Only the loads of the microgrids containing GFL 16 and GFL 27 are cut off, while GFM 9 and GFM 35 can supply power to the microgrids where they are located because they meet the transient frequency constraint. The state of the distribution network remains unchanged during the entire disaster stage.

[0141] After the disaster, two tie lines are closed to supply power to the power-off microgrids with grid-forming DGs. Due to the limitation of the transient frequency constraint, the restoration is carried out in multiple steps, and the restoration situation is shown in Table 2: Table 2 Fault restoration situation after the disaster in scenario 1

[0142] It can be seen that due to the transient frequency constraint, the restoration cannot be completed in one step. The microgrid containing GFL 16 is restored in 2 steps, while the microgrids containing GFL 11 and GFL 27 need to be restored in 3 steps because the latter contains heavier loads. It should be noted that during the fault isolation during the disaster, the circuit breakers of lines 6-16, 26-27, and 30-31 are not disconnected. However, during the post-disaster restoration stage, due to the need to meet the limitation of the transient frequency constraint, the above three will be disconnected in time period 1 and then closed respectively.

[0143] To demonstrate the effectiveness of the proposed pre-scheduling method, a basic case and two comparison cases are established for analysis and comparison. The characteristics, total operating cost, and maximum frequency change during the whole process of each case are shown in Table 3: Table 3 Characteristics, total operating cost, and maximum frequency change during the whole process of each case

[0144] First, compare Case 1 and Case 2 to analyze the significance of pre-disaster pre-scheduling considering transient frequency constraints.

[0145] Taking the microgrid with GFM 2 under Scenario 1 as an example, as Figure 4 .

[0146] If GFM 2 does not perform pre-disaster pre-scheduling but operates at full power of 200 kW, its corresponding load is 200 kW; after a fault occurs, a microgrid consisting of Nodes 9, 24, and 36 is formed. At this time, the load suddenly changes to 58.06 kW. Due to the limitation of the transient frequency constraint of the load change, the frequency change is greater than the allowed , resulting in the tripping of the generator of GFM 2, causing the microgrid to lose power and expanding the load shedding range, as Figure 5 . Therefore, even though Case 1 reduces the output of DG before the disaster and temporarily increases the power generation cost, it avoids the tripping of the network-forming power source during a longer mid-disaster stage and significantly reduces the mid-disaster load shedding cost. Therefore, the total operating cost of Case 2 is 10% more than that of Case 1. Therefore, by pre-scheduling the distribution network in advance according to disaster information and adjusting the output of each DG, the consequence of the network-forming power source exceeding the transient frequency constraint and tripping can be avoided in some scenarios, improving the resistance ability of the distribution network during the disaster.

[0147] Secondly, compare Case 1 and Case 3 to analyze the significance of transient frequency constraints during the post-disaster recovery process.

[0148] Taking the microgrid where GFM 3 is located under Scenario 1 as an example, the frequency changes during the post-disaster recovery process in two cases are obtained through simulation, as Figure 6 , it can be seen that Case 3 completes the recovery only through one time period, but its frequency parameters are much lower than the safety limit; Case 1 completes the recovery through 3 time periods, and the transient frequency characteristics of each time period are good. Therefore, although considering transient frequency constraints increases the total cost of the whole event process, it ensures the practical feasibility of the obtained solution.

[0149] In summary, a three-stage distribution network extreme event recovery method and system considering transient frequency constraints of the present invention significantly improves the resilience level of the distribution network. This method plays a role in all three stages of the disaster, and at the same time considers the transient frequency characteristics of the microgrid during the disaster and after the disaster, ensuring the feasibility of the obtained distribution network resilience improvement solution.

[0150] The above content is only to illustrate the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the claims of the present invention.

Claims

1. A three-stage distribution network extreme event recovery method considering transient frequency constraints, characterized in that: The following steps are involved: Determine the objective function of the three-stage distribution network resilience improvement mathematical model, and construct the three-stage distribution network resilience improvement mathematical model considering transient frequency constraints; Based on the constructed three-stage distribution network resilience improvement mathematical model, the on / off status of the teleswitch lines and the output of DG are changed according to the forecast situation and historical data before the disaster to adjust the power flow distribution; When a fault occurs, the protection is disconnected, so that the distribution network forms a microgrid, and the microgrid without a grid-forming DG loses all loads; After the disaster, the microgrid containing the grid-type DG supplies power to the microgrid that has lost its load through the closed interconnection line. During the load picking process, the microgrid follows the transient frequency constraints. When the microgrid load cannot be restored in one go, it is restored in sequence by time periods.

2. The three-stage distribution network extreme event recovery method considering transient frequency constraints according to claim 1 is characterized in that: The objective function is: in, The probability of occurrence of each failure scenario predicted before the disaster; , and The duration of each stage; , and is the load reduction penalty factor for each stage; is the load weight; , and Reduce the load for each stage; is the DG power generation cost coefficient at each stage; , and Make contributions to DG at each stage; , are collections of scenes and nodes respectively.

3. The three-stage distribution network extreme event recovery method considering transient frequency constraints according to claim 1 is characterized in that: Before the disaster, according to the forecast and historical data, the on / off status of the line containing the teleswitch and the output of the DG are changed to adjust the power flow distribution, as follows: The topological constraints consider active island constraints and distribution network radial constraints. The active island constraint is that the lines with teleswitch can be disconnected in advance before the disaster, so that the distribution network is decomposed into islands. The radial constraints of the distribution network satisfy the conditions that the number of closed lines is equal to the difference between the number of nodes and the number of subgraphs in the topology; the connectivity of each subgraph is satisfied; The operation constraints consider power balance constraints, adjacent node voltage constraints, line transmission limit constraints, node voltage constraints and DG output constraints.

4. The three-stage distribution network extreme event recovery method considering transient frequency constraints according to claim 3 is characterized in that: Power balance constraints: in, Pre-disaster route Transmitted active and reactive power; Pre-disaster node Active and reactive output of the included DG; Pre-disaster node The power-on state binary variable is 1 when the power is on; For Node Load; Adjacent node voltage constraints: in, Pre-disaster node Voltage; For Line Impedance; is the rated voltage of the distribution network; Line transmission limit constraints: in, is the line transmission limit; Node voltage constraints: in, and are the maximum and minimum values ​​allowed for the node voltage respectively; The DG output constraints are as follows: in, and For Node The upper limit of active and reactive output of the included DG; is the set of DGs.

5. The three-stage distribution network extreme event recovery method considering transient frequency constraints according to claim 1 is characterized in that: Constraints after a failure include: Topological constraints take into account fault propagation and quick-break protection disconnection constraints: when multiple faults occur in the distribution network, the quick-break protection closest to the fault point will be activated to cut off the corresponding line and isolate the fault, that is, the line with quick-break protection can be disconnected during the disaster; Operation constraints include power balance constraints, adjacent node voltage constraints, line transmission limit constraints, node voltage constraints, DG output constraints, and DG output constraints in the fault area; At the moment of fault occurrence, the protection disconnects and isolates the fault, so that the distribution system forms multiple microgrids. It is tested whether the grid-forming DG can continue to output power after the fault is isolated, and the load change of the microgrid at the moment of fault isolation and the grid-forming DG included in the microgrid are obtained.

6. The three-stage distribution network extreme event recovery method considering transient frequency constraints according to claim 5 is characterized in that: DG output constraints in the fault area: in, For disaster scenes Below the node The DG has made a positive contribution. For disaster scenes Below the node The DG reactive power output, , are the maximum active and reactive power outputs of each distributed power source, For disaster scenes Next Node Is it in the fault area? If the value is 1, it is in the fault area. is the collection of distribution network nodes.

7. The three-stage distribution network extreme event recovery method considering transient frequency constraints according to claim 5 is characterized in that: The transient frequency stability indicators of the microgrid include the initial frequency change rate and the lowest frequency point, the linearized initial frequency change rate constraint and the lowest frequency point constraint: in, is the threshold defined for the frequency rate of change metric, is the maximum frequency deviation of each grid-type power source or substation operation, is the response time of the unit's primary frequency regulation, For the scene Contains grid-type power supply The load change of the microgrid before and after the fault occurs. , For disaster scenes Contains grid-type power supply The equivalent inertia coefficient and damping coefficient of the microgrid, A collection of grid-type power sources. For disaster scenes Contains grid-type power supply The load of the microgrid.

8. The three-stage distribution network extreme event recovery method considering transient frequency constraints according to claim 1 is characterized in that: Post-disaster constraints include: Topological constraints, taking into account teleswitch closure, fault propagation and distribution network radial constraints; Operation constraints, including power balance constraints, adjacent node voltage constraints, line transmission limit constraints, node voltage constraints, and DG output constraints; Frequency constraint, post-disaster load recovery phase, the initial state is directly transferred from the final state of the fault isolation phase during the disaster, and the post-disaster scenario is determined Next, each period The equivalent inertia and equivalent damping coefficient of the microgrid where the grid-type DG is located are calculated to obtain the linearized initial frequency change rate constraint and the frequency minimum point constraint in the post-disaster stage.

9. The three-stage distribution network extreme event recovery method considering transient frequency constraints according to claim 8 is characterized in that: Initial frequency change rate constraint and frequency minimum point constraint after linearization: in, For post-disaster scenes Contains grid-type power supply Microgrid The load change before and after the moment of recovery, , Post-disaster scenes Contains grid-type power supply Microgrid The equivalent inertia coefficient and damping coefficient before the moment is restored, The threshold defined for the frequency change rate indicator is 0.25Hz / s. The maximum frequency deviation of each grid-type power source or substation operation is 0.5Hz. is the response time of the unit's primary frequency regulation, assuming that all units are the same. For post-disaster scenes Contains grid-type power supply Microgrid The load after the moment of recovery.

10. A three-stage distribution network extreme event restoration system considering transient frequency constraints, characterized in that: include: Construct a module, determine the objective function of the three-stage distribution network resilience improvement mathematical model, and establish a three-stage distribution network resilience improvement mathematical model considering transient frequency constraints; The pre-disaster module is based on the constructed three-stage distribution network resilience improvement mathematical model. Before the disaster, the on / off state of the teleswitch lines and the output of the DG are changed according to the forecast situation and historical data to adjust the power flow distribution; The disaster module disconnects the protection when a fault occurs, so that the distribution network forms a microgrid, and the microgrid without a grid-forming DG loses all loads; In the recovery module, after the disaster, the microgrid containing the grid-type DG supplies power to the microgrid that has lost the load through the closed interconnection line. During the load picking process, the microgrid follows the transient frequency constraints. When the microgrid load cannot be restored in one go, it is restored in sequence by time periods.

Images