A multi-stage dynamic restoration method for power distribution system considering cold load startup characteristics

Abstract

The application discloses a kind of considering the multi-stage dynamic recovery method of power distribution system starting characteristics of cold load, comprising:1 obtains the operating state when power distribution system fails;2 establish the operating model of various controllable devices installed in power distribution system;3 combined with the operating model of various devices, construct optimal load restoration model, obtain power distribution system dynamic network reconfiguration scheme, flexible device action sequence by solving optimal load restoration model, and issue to dynamic recovery model;4 combined with the operating model of equipment, considering the load restoration model of cold load starting characteristics CLPU, voltage and frequency safety, establish dynamic recovery stage model;5 complete power distribution system multi-stage dynamic recovery scheme is obtained by solving dynamic recovery model.The application can improve the recovery level of power distribution system and the utilization rate of renewable energy, thereby improve the adaptability of recovery scheme, enhance the self-repairing ability of power distribution system.

Description

Technical Field

[0001] This invention belongs to the field of power distribution system fault recovery, specifically a multi-stage dynamic recovery method for power distribution systems that takes into account cold load start-up characteristics. Background Technology

[0002] In recent years, frequent extreme disasters have posed a significant threat to the reliable power supply of power systems. Compared to transmission systems, distribution systems are directly connected to electricity users, making their reliability more critical. Furthermore, the widespread integration of distributed power sources and renewable energy sources (such as photovoltaics and wind turbines) has transformed traditional radial distribution systems into multi-source systems. The development of power electronics technology is further driving the evolution of distribution systems towards flexible, closed-loop structures. When a distribution system fails, the complex structure and control methods make fault recovery more difficult.

[0003] Addressing the aforementioned challenges and effectively utilizing the multi-source controllable resources (such as distributed resources and power electronic devices) of the power distribution system to improve its resilience under extreme events is a pressing issue. Soft switching, with its precise power flow control, rapid power transfer, and active voltage / frequency support, has broad application prospects in power distribution system fault recovery. Reconfigurable soft switching is a further improvement on multi-terminal soft switching, aiming to improve the utilization efficiency of voltage source converters without changing the total capacity of multi-terminal soft switching. This allows reconfigurable soft switching to outperform multi-terminal soft switching in scenarios with high power transmission requirements. However, in practice, introducing these new power electronic devices into power distribution system fault recovery can affect the sequence of switching operations and the actions of multiple recovery resources. Therefore, a collaborative optimization framework is urgently needed to seamlessly coordinate these processes.

[0004] On the other hand, most power distribution system restoration studies only consider constant load models, neglecting the phenomenon of cold load restoration caused by temperature-controlled load restoration. In power distribution systems, the proportion of temperature-controlled loads, represented by air conditioners, is increasing year by year, and this proportion will further increase under extreme weather conditions. However, temperature-controlled loads experience a surge in load volume shortly after commissioning, and this load peak can affect the safety of the power distribution system during power restoration. Ignoring this characteristic will lead to restoration schemes that deviate from practical applications. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies by proposing a multi-stage dynamic recovery method for power distribution systems that considers cold load start-up characteristics. The aim is to leverage the high-power transmission capabilities of reconfigurable soft switches, precise power flow control, rapid power transfer, and active voltage / frequency support to effectively eliminate system voltage issues during recovery. By integrating controllable resources of the power distribution system, this multi-stage dynamic recovery method enhances adaptability to cold load recovery phenomena, thereby accelerating the recovery of power-loss loads.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] The present invention provides a multi-stage dynamic recovery method for power distribution systems that considers cold load start-up characteristics, characterized by the following steps:

[0008] S1: Obtain the operating status of the power distribution system when a fault occurs, including: the location and number of the faulty line in the power distribution system, and the location and number of the fault-free line.

[0009] S2: When a power distribution system fails, acquire information on wind turbines (Wind), photovoltaic equipment (PV), reconfigurable soft switches (R-SOP), and user load demand information for each time period (L); thereby establishing an operation model for reconfigurable soft switches (R-SOP), a power distribution system fault reconfiguration model, and a power distribution system fault flow model.

[0010] S3: Modeling various adjustable devices, including: operating models of on-load tap-changing transformers (OLTCs), distributed generation (DGs), switchable capacitor banks (CBs), and energy storage systems (ESSs).

[0011] S4: After constructing and solving the optimal load recovery stage model, obtain the dynamic network reconfiguration scheme, energy storage capacity pre-allocation plan and discrete equipment action scheme of the power distribution system, and send them to the dynamic recovery stage model;

[0012] S5: Considering the load recovery characteristics of cold load start-up, establish frequency safety response constraints for the power distribution system during power outage load recovery and update the operation model of adjustable equipment, thereby constructing a dynamic recovery phase model:

[0013] S6: After establishing and solving the dynamic recovery phase model, the action sequence of reconfigurable soft switching, distributed power supply and controllable resources under the dynamic recovery phase is obtained, thus obtaining a complete fault dynamic recovery scheme.

[0014] S7: After converting the multi-stage dynamic recovery constraints in the optimal load recovery stage model and the dynamic recovery stage model into mixed integer second-order cone programming constraints, the dynamic recovery scheme of the power distribution system is obtained, which includes the operation of reconfigurable soft switching, on-load tap-changing transformer, switchable capacitor, energy storage system, load switch, sectionalizing switch, and tie switch.

[0015] The multi-stage dynamic recovery method for power distribution systems considering cold load start-up characteristics described in this invention is also characterized in that S2 includes the following steps:

[0016] S2-1: Using equations (1)-(6), the operating model of the reconfigurable soft switch R-SOP is obtained:

[0017] (1)

[0018] (2)

[0019] (3)

[0020] (4)

[0021] (5)

[0022] (6)

[0023] In equations (1)-(6), This represents the set of nodes connected to the voltage source converter (VSC). This represents the set of all voltage source converters; for Time Node Total loss of all connected VSCs The total DC-side active power of all VSCs, The total AC-side active power of all VSCs; for Time Node Apparent power transmitted via reconfigurable soft-switching R-SOP for Time Node Reactive power transmitted via reconfigurable soft switch R-SOP; for Time Node With voltage source converter The connected state; The operating loss factor for each voltage source converter; Voltage source converter The capacity;

[0024] S2-2: Using equations (7)-(12), establish a fault reconfiguration model for a power distribution system containing a reconfigurable soft switch R-SOP:

[0025] (7)

[0026] (8)

[0027] (9)

[0028] (10)

[0029] (11)

[0030] (12)

[0031] In equations (7)-(12), It is a set of distribution line nodes. For nodes of power distribution lines, ; Represents a node To the node The route, Represents all slave nodes To the node The route; It is a node With nodes Between lines The connected state; It is the number of nodes in the power distribution system; This refers to the number of substations in the power distribution system. It is the number of ports of the reconfigurable soft switch R-SOP; It is a node The on / off state of the connected reconfigurable soft switch R-SOP port, when R-SOP acts as a virtual power supply output and is positive. It equals 1, otherwise it equals 0; It is a line The virtual trend It is a line Virtual trends on the internet; yes Time Node The virtual current generated by the virtual power source; It is a node Virtual load demand; M is a constant;

[0032] S2-3: Using equations (13)-(22), a fault flow model for a power distribution system containing reconfigurable soft switches (R-SOPs) is obtained:

[0033] (13)

[0034] (14)

[0035] (15)

[0036] (16)

[0037] (17)

[0038] (18)

[0039] (19)

[0040] (20)

[0041] (twenty one)

[0042] (twenty two)

[0043] In equations (13)-(22), and They are respectively Timetable The active and reactive power transmitted upstream; and The lines are respectively Resistance and reactance; for Timetable The current transmitted upwards; and They are respectively Time Node The injected active and reactive power; and They are respectively Timetable The active and reactive power transmitted upstream; , They are respectively Time Node , Voltage at the point; and The lines are respectively Resistance and reactance; for Timetable The current transmitted upwards; for Time Node With nodes Between lines The connected state; and They are respectively Time Node The reduction in active power output of photovoltaic (PV) equipment and the reduction in active power output of photovoltaic equipment; and They are respectively Time Node The reduction in active power output of the wind turbine (Wind) and the reduction in active power output of the wind turbine; , They are Time Node The active and reactive power outputs of the distributed generation (DG); , for Time Node The active and reactive power outputs of the R-SOP; and They are respectively Time Node The reactive power output of photovoltaic (PV) equipment and wind turbine (Wind) is calculated. and They are respectively Time Node The active and reactive power consumed by load L; yes Time Node The reactive power output of the capacitor CBs can be switched on and off at the location; for Time Node The status of the load switch that controls the on / off state of the load; and These are the upper and lower limits of the node voltage in the power distribution system, respectively. This is the upper limit of the line current in the power distribution system.

[0044] Furthermore, S3 includes the following steps:

[0045] S3-1: Establish the operating model of the on-load tap-changing transformer (OLTC) using equations (23) and (24):

[0046] (twenty three)

[0047] (twenty four)

[0048] In equations (23)-(24), for Time Node The voltage at the auxiliary node aux is equal to the voltage on the secondary side of the on-load tap-changing transformer. for Timetable The tap position of the on-load tap-changing transformer (OLTC); for Timetable The voltage regulation rate of the on-load tap-changing transformer OLTC; For the line The initial voltage regulation rate of the on-load tap-changing transformer OLTC; For the line The change in voltage regulation at adjacent tap positions; A set of integer variables;

[0049] S3-2: Using equations (25)-(28), construct the operation model of distributed generation (DG) and the operation model of switchable capacitor banks:

[0050] (25)

[0051] (26)

[0052] (27)

[0053] (28)

[0054] In equations (25)-(28), , They are Time Node The active and reactive power outputs of the distributed generation (DG); for Time Node The distributed generation (DG) is in the on state; , These are the maximum active power output and maximum reactive power output of the distributed generation (DG), respectively. yes Time Node The reactive power output of the capacitor CBs can be switched on and off at the location; It refers to the capacitance of each group of switchable capacitors (CBs). yes Time Node The number of switchable capacitor banks that can be connected at a given location. This is the maximum number of switchable capacitor banks that can be switched on;

[0055] S3-3: Construct the operating model of the Energy Storage System (ESS) using equations (29)-(33):

[0056] (29)

[0057] (30)

[0058] (31)

[0059] (32)

[0060] (33)

[0061] In equations (29)-(33), , These are the minimum and maximum charging power values ​​of the energy storage system (ESS), respectively. , These are the minimum and maximum discharge power of the energy storage system (ESS), respectively. for Auxiliary variables are set in real time, so that when the energy storage system (ESS) is charging, =1, when ESS discharges, let =0; , For example, the energy storage system ESS The charging power and discharging power at any given time; , , These represent the minimum, maximum, and initial values ​​of the energy storage state of charge, respectively. , These represent the total capacity of the energy storage system (ESS) and... The capacity of the ESS (Energy Storage System); for The capacity of the ESS (Energy Storage System); , These are the charging efficiency and discharging efficiency of the energy storage system (ESS), respectively. For time step.

[0062] Furthermore, S4 uses equation (34) to establish the objective function of the optimal load recovery stage model. Equations (7)-(12), (13)-(22), (1), (2), (4)-(6), (33), and (23)-(32) are used as constraints for the optimal load recovery stage model.

[0063] (34)

[0064] In equation (34), , , These are, respectively, the operating losses of the power distribution system, the load reduction, and the reduction in renewable energy output. This is a weighting factor for the operating losses of the power distribution system. The weighting factor for load reduction. Weighting coefficients for the reduction in power output from new energy sources; This refers to the time of failure.

[0065] Furthermore, S5 includes the following steps:

[0066] S5-1: Establish a load recovery model considering cold load start-up characteristics using equations (35)-(38):

[0067] (35)

[0068] (36)

[0069] (37)

[0070] (38)

[0071] In equations (35)-(38), This indicates the cold start load recovery phase. , They are stage, Phase Node The multiple of the load demand under a relatively stable cold start load condition; yes Phase Node The change in the cold start load demand ratio; , They are nodes The ratio of peak demand and stable demand relative to normal value during cold start; It is a node The attenuation factor of the cold negative start-up load; It is a node The cold start load begins to diversify from its initial state. The duration of the phase; It is a node The duration of the load recovery process from the start of the new state varies; It is a piecewise function;

[0072] S5-2: Based on the proportions of cold load and normal load in the power distribution system, the nodes containing unrecovered cold start loads are modeled using equations (39)-(41):

[0073] (39)

[0074] (40) (41)

[0075] In equations (39)-(41), , They represent Time Node The active power demand and reactive power demand of the actual load L; and They are respectively Time Node The active and reactive power consumed by load L; for Time Node The status of the load switch that controls the on / off state of the load; for Time Node The status of the load switch that controls the on / off state of the load; Is the cooling load at the node The proportion;

[0076] S5-3: Construct frequency response constraints using equation (42):

[0077] (42)

[0078] In equation (42), It is the collection of load nodes in the power distribution system that are not supplied by the main grid. It is a coefficient. It is the maximum active power transmitted by the reconfigurable soft switch R-SOP. It is the maximum active power output of the distributed generation (DG);

[0079] S5-4: In the dynamic recovery phase at a small time scale, power ramping constraints for energy storage systems and distributed power sources are constructed using equations (43)-(46):

[0080] (43)

[0081] (44)

[0082] (45)

[0083] (46)

[0084] In equations (43)-(46), , For example, the energy storage system ESS The charging power and discharging power at any given time; , For example, the energy storage system ESS The charging power and discharging power at any given time; This is a limit value for the variation of energy storage power; yes Time Node The active power output of the distributed generation (DG); yes Time Node The active power output of the distributed generation (DG); For nodes The ramp power allowable value for distributed generation (DG). The time scale is used to solve for the dynamic recovery phase.

[0085] Furthermore, in S6, the objective function of the dynamic recovery stage model is established using equation (47), and equations (13)-(22), (42), (1), (2), (4)-(6), (33), (23)-(32), (43)-(46), and (35)-(41) are used as constraints of the dynamic recovery stage model:

[0086] (47)

[0087] In equation (47), It is the weighting coefficient for the energy deviation value of the two-stage energy storage.

[0088] Furthermore, S7 transforms the multi-stage dynamic recovery constraints into mixed-integer second-order cone programming constraints using the following steps:

[0089] S7-1: Two nonlinear variables and Replace them with two linear variables respectively and The big-M method is used to relax the fault flow constraints (13)-(15) and (21)-(22) to transform them into linear constraints, thereby using equations (48)-(52) to construct constraints that conform to the fault scenario:

[0090] (48)

[0091] (49)

[0092] (50)

[0093] (51)

[0094] (52)

[0095] In equations (48)-(52), and The square of the voltage at node i at time t and the square of the branch current between node i and node j at time t, respectively.

[0096] S7-2: Using equation (53), equation (16) is transformed into a second-order cone constraint:

[0097] (53)

[0098] S7-3: Modify equation (23) to construct power flow constraints using equation (54);

[0099] (54)

[0100] In equation (54), Represented as Time Node The square of the voltage at the auxiliary node aux;

[0101] S7-4: Introduce auxiliary 0 / 1 variables and auxiliary voltage variables, and obtain the results using equations (55) and (56). Transformed constraints:

[0102] (55)

[0103] (56)

[0104] In equation (55), For the line The maximum value at the OLTC tap position;

[0105] S7-5: Constructing linearization constraints using equations (58) and (59):

[0106] (58)

[0107] (59)

[0108] In equations (58) and (59), for Time corresponding node To the node On the line tap position The closed state; if closed, then The value is 1; if it is turned on, then... =0, for Time corresponding node To the node Tap position on the line The square of the voltage applied;

[0109] S7-6: Using equation (60), the capacity constraint of R-SOP is transformed into a rotating cone constraint:

[0110] (60)

[0111] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the multi-stage dynamic recovery method of the power distribution system, and the processor is configured to execute the program stored in the memory.

[0112] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs the steps of the multi-stage dynamic recovery method for the power distribution system.

[0113] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0114] 1. This invention proposes a multi-stage dynamic recovery model that adapts to the cold load recovery phenomenon caused by temperature-controlled load recovery. It takes into account the actual cold load recovery phenomenon caused by temperature-controlled load recovery, thereby effectively meeting the actual load operation requirements and realizing the reliable and adaptive recovery of the power distribution system.

[0115] 2. This invention integrates controllable equipment scheduling and dynamic network reconfiguration, establishing a multi-device collaborative optimization framework. This invention enables various flexible devices to coordinate at different time scales based on their own characteristics and operational constraints. The recovery method integrates the reconfiguration of asymmetric voltage source converters and the sequential execution of responses to cold load recovery phenomena, thereby improving the adaptability of the recovery scheme, enhancing the self-healing capability of the distribution system, improving power flow distribution, and increasing the level of distribution service recovery.

[0116] 3. This invention takes into account the voltage and frequency safety of the power distribution system during the fault recovery process, and can ensure system safety during the recovery process. It can carry out fault recovery in stages and has better applicability. Attached Figure Description

[0117] Figure 1 This is a typical cooling load characteristic recovery curve;

[0118] Figure 2 This is the modified topology diagram of the IEEE 33-node fault system;

[0119] Figure 3 This is a diagram of the controllable resource operation scheme for the power distribution system;

[0120] Figure 4 It is the total capacity of the voltage source converters connected to each feeder during the fault recovery process of the reconfigurable soft switch;

[0121] Figure 5 This is a schematic diagram showing the percentage of load recovery during each fault period in Case 1 and Case 2;

[0122] Figure 6 This is a schematic diagram of the load recovery amount under Case 1 and Case 2;

[0123] Figure 7 This is a flowchart of the method for implementing a multi-stage dynamic recovery model. Detailed Implementation

[0124] In this embodiment, a multi-stage dynamic recovery method for distribution systems considering cold load recovery, aided by reconfigurable soft switches, is proposed. Taking into account the dynamic recovery characteristics of cold-start load recovery and combining the reconfigurable intelligent soft switch reconfiguration, distribution network topology changes, and the synergistic effect of flexible resources, a multi-stage dynamic recovery model is constructed: an optimal load recovery stage and a dynamic recovery stage. This model responds to cold-start load demands on a faster time scale and performs fault recovery in a reliable and adaptive manner, thereby improving the recovery level of the distribution system and the utilization rate of renewable energy, thus enhancing the adaptability of the recovery scheme and strengthening the self-healing capability of the distribution system. Specifically, as... Figure 7 As shown, the method includes the following steps:

[0125] S1: Obtain the operating status of the power distribution system during a fault, including: the location and number of the faulty line in the power distribution system, and the location and number of the fault-free line; to calculate the power loss area after the power distribution system fault is isolated;

[0126] S2: When a power distribution system fails, acquire information on wind turbines (Wind), photovoltaic equipment (PV), reconfigurable soft switch (R-SOP), and user load demand information for each time period (L); thereby establishing an operating model for the reconfigurable soft switch (R-SOP), a power distribution system fault reconfiguration model, and a power distribution system fault flow model.

[0127] S2-1: Using equations (1)-(6), the operating model of the reconfigurable soft switch R-SOP is obtained:

[0128] (1)

[0129] (2)

[0130] (3)

[0131] (4)

[0132] (5)

[0133] (6)

[0134] In equations (1)-(6), This represents the set of nodes connected to the voltage source converter (VSC). This represents the set of all voltage source converters; for Time Node Total loss of all connected VSCs The total DC-side active power of all VSCs, The total AC-side active power of all VSCs; for Time Node Apparent power transmitted via reconfigurable soft-switching R-SOP for Time Node Reactive power transmitted via reconfigurable soft switch R-SOP; for Time Node With voltage source converter The connected state; The operating loss factor for each voltage source converter; Voltage source converter The capacity.

[0135] S2-2: A power distribution system fault reconfiguration model is established using the virtual power flow method. Equations (7)-(12) are used to establish a power distribution system fault reconfiguration model containing reconfigurable soft switches R-SOP, so as to obtain the power distribution system fault reconfiguration scheme during the recovery process:

[0136] (7)

[0137] (8)

[0138] (9)

[0139] (10)

[0140] (11)

[0141] (12)

[0142] In equations (7)-(12), It is a set of distribution line nodes. For nodes of power distribution lines, ; Represents a node To the node The route, Represents all slave nodes To the node The route; It is a node With nodes Between lines The connected state; It is the number of nodes in the power distribution system; This refers to the number of substations in the power distribution system. It is the number of ports of the reconfigurable soft switch R-SOP; It is a node The on / off state of the connected reconfigurable soft switch R-SOP port, when R-SOP acts as a virtual power supply output and is positive. It equals 1, otherwise it equals 0; It is a line The virtual trend It is a line Virtual trends on the internet; yes Time Node The virtual current generated by the virtual power source; It is a node The virtual load demand; M is a constant.

[0143] S2-3: Using equations (13)-(22), a fault flow model for a power distribution system containing reconfigurable soft switches (R-SOPs) is obtained:

[0144] (13)

[0145] (14)

[0146] (15)

[0147] (16)

[0148] (17)

[0149] (18)

[0150] (19)

[0151] (20)

[0152] (twenty one)

[0153] (twenty two)

[0154] In equations (13)-(22), and They are respectively Timetable The active and reactive power transmitted upstream; and The lines are respectively Resistance and reactance; for Timetable The current transmitted upwards; and They are respectively Time Node The injected active and reactive power; and They are respectively Timetable The active and reactive power transmitted upstream; , They are respectively Time Node , Voltage at the point; and The lines are respectively Resistance and reactance; for Timetable The current transmitted upwards; for Time Node With nodes Between lines The connected state; and They are respectively Time Node The reduction in active power output of photovoltaic (PV) equipment and the reduction in active power output of photovoltaic equipment; and They are respectively Time Node The reduction in active power output of the wind turbine (Wind) and the reduction in active power output of the wind turbine; , They are Time Node The active and reactive power outputs of the distributed generation (DG); , for Time Node The active and reactive power outputs of the R-SOP; and They are respectively Time Node The reactive power output of photovoltaic (PV) equipment and wind turbine (Wind) is calculated. and They are respectively Time Node The active and reactive power consumed by load L; yes Time Node The reactive power output of the capacitor CBs can be switched on and off at the location; for Time Node The status of the load switch that controls the on / off state of the load; and These are the upper and lower limits of the node voltage in the power distribution system, respectively. This is the upper limit of the line current in the power distribution system.

[0155] S3: Modeling various adjustable devices, including: operating models of on-load tap-changing transformers (OLTCs), distributed generation (DGs), switchable capacitor banks (CBs), and energy storage systems (ESSs).

[0156] S3-1: An auxiliary node aux is introduced on the secondary side of the on-load tap-changing transformer (OLTC). After neglecting the losses of the OLTC itself, the operation model of the on-load tap-changing transformer OLTC is established using equations (23)-(24):

[0157] (twenty three)

[0158] (twenty four)

[0159] In equations (23)-(24), for Time Node The voltage at the auxiliary node aux is equal to the voltage on the secondary side of the on-load tap-changing transformer. for Timetable The tap position of the on-load tap-changing transformer (OLTC); for Timetable The voltage regulation rate of the on-load tap-changing transformer OLTC; For the line The initial voltage regulation rate of the on-load tap-changing transformer OLTC; For the line The change in voltage regulation at adjacent tap positions; It is a set of integer variables.

[0160] S3-2: Using equations (25)-(28), construct the operation model of distributed generation (DG) and the operation model of switchable capacitor banks:

[0161] (25)

[0162] (26)

[0163] (27)

[0164] (28)

[0165] In equations (25)-(28), , They are Time Node The active and reactive power outputs of the distributed generation (DG); for Time Node The distributed generation (DG) is in the on state; , These are the maximum active power output and maximum reactive power output of the distributed generation (DG), respectively. yes Time Node The reactive power output of the capacitor CBs can be switched on and off at the location; It refers to the capacitance of each group of switchable capacitors (CBs). yes Time Node The number of switchable capacitor banks that can be connected at a given location. It is the maximum number of switchable capacitor banks that can be switched on.

[0166] S3-3: Using equations (29)-(33), an operating model of the energy storage system ESS is constructed. By installing the energy storage system on the DC side of the R-SOP, the R-SOP can have energy storage capabilities and accurately control the power flow in both spatial and temporal dimensions. Equation (3) is modified to Equation (33):

[0167] (29)

[0168] (30)

[0169] (31)

[0170] (32)

[0171] (33)

[0172] In equations (29)-(33), , These are the minimum and maximum charging power values ​​of the energy storage system (ESS), respectively. , These are the minimum and maximum discharge power of the energy storage system (ESS), respectively. for Auxiliary variables are set in real time, so that when the energy storage system (ESS) is charging, =1, when ESS discharges, let =0; , For example, the energy storage system ESS The charging power and discharging power at any given time; , , These represent the minimum, maximum, and initial values ​​of the energy storage state of charge, respectively. , These represent the total capacity of the energy storage system (ESS) and... The capacity of the ESS (Energy Storage System); for The capacity of the ESS (Energy Storage System); , These are the charging efficiency and discharging efficiency of the energy storage system (ESS), respectively. For time step.

[0173] S4: After constructing and solving the optimal load recovery stage model, obtain the dynamic network reconfiguration scheme, energy storage capacity pre-allocation plan and discrete equipment action scheme of the power distribution system, and send them to the dynamic recovery stage model;

[0174] S4-1: Using equation (34) to establish the objective function of the optimal load recovery stage model :

[0175] (34)

[0176] In equation (34), , , These are, respectively, the operating losses of the power distribution system, the load reduction, and the reduction in renewable energy output. This is a weighting factor for the operating losses of the power distribution system. The weighting factor for load reduction. Weighting coefficients for the reduction in power output from new energy sources; For the time of failure;

[0177] S4-2: Equations (7)-(12), (13)-(22), (1), (2), (4)-(6), (33), and (23)-(32) are used as constraints for the optimal load recovery stage model.

[0178] S5: Considering the load recovery characteristics of cold load start-up, establish frequency safety response constraints for the power distribution system during power outage load recovery and update the operation model of adjustable equipment, thereby constructing a dynamic recovery phase model:

[0179] S5-1: Adopted Figure 1 The exponential cold-start load model shown is used to simulate the cold-start load demand in the actual power distribution system. A load recovery model considering the cold-start characteristics is established using equations (35)-(38):

[0180] (35)

[0181] (36)

[0182] (37)

[0183] (38)

[0184] In equations (35)-(38), This indicates the cold start load recovery phase. , They are stage, Phase Node The multiple of the load demand under a relatively stable cold start load condition; yes Phase Node The change in the cold start load demand ratio; , They are nodes The ratio of peak demand and stable demand relative to normal value during cold start; It is a node The attenuation factor of the cold negative start-up load; It is a node The cold start load begins to diversify from its initial state. The duration of the phase; It is a node The duration of the load recovery process from the start of the new state varies; It is a piecewise function.

[0185] S5-2: Based on the proportions of cold load and normal load in the power distribution system, the load modeling in equations (17)-(18) needs to be modified in the dynamic recovery model. Cold start loads that have been fully recovered can be treated as normal loads. Cold start loads should not be reduced when they have not been fully recovered. Equations (39)-(41) are used to model nodes containing cold start loads that have not been recovered.

[0186] (39)

[0187] (40) (41)

[0188] In equations (39)-(41), , They represent Time Node The active power demand and reactive power demand of the actual load L; and They are respectively Time Node The active and reactive power consumed by load L; for Time Node The status of the load switch that controls the on / off state of the load; for Time Node The status of the load switch that controls the on / off state of the load; Is the cooling load at the node The percentage.

[0189] S5-3: To reduce the difficulty of solving the model considering the frequency constraint recovery scheme, a simplified frequency response rate constraint is used to approximate the frequency response. The frequency response rate constraint is constructed using equation (42):

[0190] (42)

[0191] In equation (42), It is the collection of load nodes in the power distribution system that are not supplied by the main grid. It is a coefficient. It is the maximum active power transmitted by the reconfigurable soft switch R-SOP. It is the maximum active power output of the distributed generation (DG);

[0192] S5-4: In the dynamic recovery phase at a small time scale, power ramping constraints for energy storage systems and distributed power sources are constructed using equations (43)-(46):

[0193] (43)

[0194] (44)

[0195] (45)

[0196] (46)

[0197] In equations (43)-(46), , For example, the energy storage system ESS The charging power and discharging power at any given time; , For example, the energy storage system ESS The charging power and discharging power at any given time; This is a limit value for the variation of energy storage power; yes Time Node The active power output of the distributed generation (DG); yes Time Node The active power output of the distributed generation (DG); For nodes The ramp power allowable value for distributed generation (DG). The time scale is used to solve for the dynamic recovery phase.

[0198] S6: After establishing and solving the dynamic recovery phase model, the action sequence of reconfigurable soft switching, distributed power supply and controllable resources under the dynamic recovery phase is obtained, thus obtaining a complete fault dynamic recovery scheme.

[0199] S6-1: Establish the objective function of the dynamic recovery stage model using equation (47):

[0200] (47)

[0201] In equation (47), The weighting coefficient for the energy deviation value of the two-stage energy storage;

[0202] S6-2: Equations (13)-(22), (42), (1), (2), (4)-(6), (33), (23)-(32), (43)-(46), (35)-(41) are used as constraints for the dynamic recovery stage model.

[0203] S7: After converting the multi-stage dynamic recovery constraints in the optimal load recovery stage model and the dynamic recovery stage model into mixed integer second-order cone programming constraints, the dynamic recovery scheme of the power distribution system is obtained, which includes the operation of reconfigurable soft switching, on-load tap-changing transformer, switchable capacitor, energy storage system, load switch, sectionalizing switch, and tie switch.

[0204] S7-1: Two nonlinear variables and Replace them with two linear variables respectively and The big-M method is used to relax the fault flow constraints (13)-(15) and (21)-(22) to transform them into linear constraints, thereby using equations (48)-(52) to construct constraints that conform to the fault scenario:

[0205] (48)

[0206] (49)

[0207] (50)

[0208] (51)

[0209] (52)

[0210] In equations (48)-(52), and Let the square of the voltage at node i at time t be equal to the square of the branch current between node i and node j at time t.

[0211] S7-2: Using equation (53), equation (16) is transformed into a second-order cone constraint:

[0212] (53)

[0213] S7-3: Modify equation (23) to construct power flow constraints using equation (54);

[0214] (54)

[0215] In equation (54), Represented as Time Node The square of the voltage at the auxiliary node aux;

[0216] S7-4: Introduce auxiliary 0 / 1 variables and auxiliary voltage variables, and obtain the results using equations (55) and (56). Transformed constraints:

[0217] (55)

[0218] (56)

[0219] In equation (55), For the line The maximum value at the OLTC tap position;

[0220] S7-5: Constructing linearization constraints using equations (58) and (59):

[0221] (58)

[0222] (59)

[0223] In equations (58) and (59), for Time corresponding node To the node On the line tap position The closed state; if closed, then The value is 1; if it is turned on, then... =0, for Time corresponding node To the node Tap position on the line The square of the voltage applied.

[0224] S7-6: Using equation (60), the capacity constraint of R-SOP is transformed into a rotating cone constraint:

[0225] (60)

[0226] By using the above method to transform the multi-stage dynamic recovery constraint into a mixed integer second-order cone programming problem, and by solving the optimal load recovery stage and the dynamic recovery stage with the help of a solver, a dynamic recovery scheme for the power distribution system can be obtained, which includes the operation of reconfigurable soft switches, on-load tap-changing transformers, switchable capacitors, energy storage systems, load switches, sectionalizing switches, and tie switches.

[0227] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0228] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

[0229] To enable those skilled in the art to better understand the present invention, the numerical example analysis includes the following components:

[0230] I. Case Description and Simulation Result Analysis

[0231] To verify its effectiveness, this invention used, for example... Figure 2 The modified IEEE 33-node fault system topology diagram shown is used for example analysis. Photovoltaic and wind turbine systems, each with a capacity of 2 MVA, are deployed at nodes 16 and 31, with a power factor of 0.85. Distributed generation and switchable capacitors are located at nodes 27 and 28, respectively. The maximum active power output of the distributed generation is 0.35 MW, and the maximum reactive power output is 0.35 MVar. The switchable capacitors can be connected in batches of 0.15 MVar, with a maximum of 4 sets of capacitors. The cold start load is set to decay to a stable value after 10 minutes. The total capacity of the 4-port reconfigurable soft switch is 4 MVA. The capacity allocation of each voltage source converter port adopts the "golden ratio" allocation method, which is 0.5, 0.309, 0.118, and 0.073 times the total capacity, respectively. Nodes selectable by the feeder selector switch are located at nodes 12, 18, 22, and 33. M is set to 1000. The voltage amplitude is [0.95, 1.05] pu. The time scales for the two stages are set to 30 minutes and 2 minutes, respectively. The simulation scenario involves a permanent fault occurring on lines 2 and 25 of the test system at 8:00 AM due to extreme weather. After fault isolation, the power distribution system begins self-healing recovery. The fault repair time for the test system is assumed to be 4 hours.

[0232] To verify the effectiveness of the multi-stage dynamic recovery scheme described in the invention, two schemes, Case 1 and Case 2, were set up for comparison in the calculation example section.

[0233] Case 1: Fault recovery method for power distribution system with 4-port reconfigurable soft switch. This method ignores the influence of cold start load characteristics, so a long-term recovery scheme is adopted.

[0234] Case 2: A multi-stage dynamic recovery solution with 4-port reconfigurable soft switch-assisted dynamic repair.

[0235] The simulation program was implemented in a Matlab environment on a computer with 64-bit Windows, an Intel(R) Core™ i5 CPU @ 3.5GHz, and 8GB of RAM. The solution was obtained using the YALMIP toolbox and the Gurobi solver.

[0236] exist Figure 2 The IEEE 33-node test system shown above executes both schemes simultaneously. Specific statistical data for the two schemes are shown in Table 1.

[0237] Table 1

[0238] Loss of load / MWh Average voltage deviation / % System losses / MWh New energy reduction / MWh Case 1 3.2737 3.6574 1.2433 2.2901 Case 2 0.1464 3.6640 0.3953 0

[0239] As shown in Table 1, both cases maintain good voltage performance during fault recovery, with the average system voltage deviation less than 5%, indicating that the reconfigurable soft switch has good voltage regulation capabilities. Case 2, employing a multi-stage dynamic recovery scheme, outperforms Case 1 in improving load recovery, reducing system losses, and promoting renewable energy absorption. Case 2, leveraging the reconfigurable design of the soft switch, achieves flexible allocation of voltage source converter capacity, increasing the transmission power of the reconfigurable soft switch. During the entire fault recovery process, the load loss is only 0.1464 MWh, significantly less than the other case, and it achieves complete renewable energy absorption. Therefore, the recovery method described in this invention utilizes the synergistic benefits of reconfigurable soft switch control scheduling and network topology changes, adapting to the multi-stage dynamic recovery model of cold-start load characteristics, thereby effectively meeting actual load operation behavior and achieving reliable and adaptive recovery of the distribution system.

[0240] like Figure 3 As shown, various flexible devices coordinate at different time scales based on their own characteristics and operational constraints, thereby improving power flow distribution in the power grid and enhancing the level of distribution service restoration. Figure 4 It can be seen that the total capacity of the voltage source converters connected to each feeder during the fault recovery process of the reconfigurable soft switch shows that the reconfigurable soft switch can dynamically allocate the total capacity of the voltage source converters connected to each feeder according to the actual power transmission requirements of the feeder.

[0241] Depend on Figure 5 It is evident that neither of the two case studies initially implemented during fault recovery could immediately achieve a high level of recovery. This is because the power outage area primarily relies on reconfigurable soft switches or power transfer from the main grid, and frequency stability in the outage area must be considered during recovery, thus limiting the load that can be restored in a single step. Furthermore, due to the cold-start characteristics of loads, the power demand during the initial recovery phase is significantly greater than the demand during stable operation. Reconfigurable soft switches cannot exceed the capacity limits of the voltage source converter devices, thus hindering the recovery of more loads. Of the two cases, Case 2 demonstrated the best recovery performance. Case 1, by failing to consider the cold-start load characteristics and employing a longer timescale in its recovery plan, resulted in a significantly inferior recovery performance compared to Case 2.

[0242] Depend on Figure 6As can be seen, unlike Case 1, Case 2, after considering the cold start load characteristics and frequency response constraints during the recovery process, adopted a sequential recovery approach, performing fault recovery step by step, which has better applicability. In the test scenario, the load recovery amount in each time period of Case 2 is higher than that in Case 1. Case 1, because it did not consider the cold start load characteristics and adopted a long-term recovery scheme, with the load switch actuating once every 30 minutes, could not close according to the expected recovery scheme during actual recovery, and the system could not achieve the expected recovery target.

[0243] In this specification, the illustrative descriptions of the invention are not necessarily directed at the same embodiments or examples. Those skilled in the art can combine and integrate the different embodiments or examples described in this specification. Furthermore, the embodiments in this specification are merely enumerations of implementation forms of the inventive concept, and the scope of protection of the invention should not be considered as limited to the specific forms stated in the embodiments. The scope of protection of the invention also includes equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A multi-stage dynamic recovery method for a power distribution system considering cold load start-up characteristics, characterized in that, Includes the following steps: S1: Obtain the operating status of the power distribution system when a fault occurs, including: the location and number of the faulty line in the power distribution system, and the location and number of the fault-free line. S2: When a power distribution system fails, acquire information on wind turbines (Wind), photovoltaic equipment (PV), reconfigurable soft switches (R-SOP), and user load demand information for each time period (L); thereby establishing an operation model for reconfigurable soft switches (R-SOP), a power distribution system fault reconfiguration model, and a power distribution system fault flow model. S3: Modeling various adjustable devices, including: operating models of on-load tap-changing transformers (OLTCs), distributed generation (DGs), switchable capacitor banks (CBs), and energy storage systems (ESSs). S4: After constructing and solving the optimal load recovery stage model, obtain the dynamic network reconfiguration scheme, energy storage capacity pre-allocation plan and discrete equipment action scheme of the power distribution system, and send them to the dynamic recovery stage model; S5: Considering the load recovery characteristics of cold load start-up, establish frequency safety response constraints for the power distribution system during power outage load recovery and update the operation model of adjustable equipment, thereby constructing a dynamic recovery phase model: S5-1: Establish a load recovery model considering cold load start-up characteristics using equations (35)-(38): (35) (36) (37) (38) In equations (35)-(38), This indicates the cold start load recovery phase. , They are stage, Phase Node The multiple of the load demand under a relatively stable cold start load condition; yes Phase Node The change in the cold start load demand ratio; , They are nodes The ratio of peak demand and stable demand relative to normal value during cold start; It is a node The attenuation factor of the cold negative start-up load; It is a node The cold start load begins to diversify from its initial state. The duration of the phase; It is a node The duration of the load recovery process from the start of the new state varies; It is a piecewise function; S5-2: Based on the proportions of cold load and normal load in the power distribution system, the nodes containing unrecovered cold start loads are modeled using equations (39)-(41): (39) (40) (41) In equations (39)-(41), , They represent Time Node The active power demand and reactive power demand of the actual load L; and They are respectively Time Node The active and reactive power consumed by load L; for Time Node The status of the load switch that controls the on / off state of the load; for Time Node The status of the load switch that controls the on / off state of the load; Is the cooling load at the node The proportion; S5-3: Construct frequency response constraints using equation (42): (42) In equation (42), It is the collection of load nodes in the power distribution system that are not supplied by the main grid. It is a coefficient. It is the maximum active power transmitted by the reconfigurable soft switch R-SOP. It is the maximum active power output of the distributed generation (DG); S5-4: In the dynamic recovery phase at a small time scale, power ramping constraints for energy storage systems and distributed power sources are constructed using equations (43)-(46): (43) (44) (45) (46) In equations (43)-(46), , For example, the energy storage system ESS The charging power and discharging power at any given time; , For example, the energy storage system ESS The charging power and discharging power at any given time; This is a limit value for the variation of energy storage power; yes Time Node The active power output of the distributed generation (DG); yes Time Node The active power output of the distributed generation (DG); For nodes The ramp power allowable value for distributed generation (DG). Solving for the time scale in the dynamic recovery phase; S6: After establishing and solving the dynamic recovery phase model, the action sequence of reconfigurable soft switching, distributed power supply and controllable resources under the dynamic recovery phase is obtained, thus obtaining a complete fault dynamic recovery scheme. S7: After converting the multi-stage dynamic recovery constraints in the optimal load recovery stage model and the dynamic recovery stage model into mixed integer second-order cone programming constraints, the dynamic recovery scheme of the power distribution system is obtained, which includes the operation of reconfigurable soft switching, on-load tap-changing transformer, switchable capacitor, energy storage system, load switch, sectionalizing switch, and tie switch. S7-1: Two nonlinear variables and Replace them with two linear variables respectively and The big-M method is used to relax the fault flow constraints (13)-(15) and (21)-(22) to transform them into linear constraints, thereby using equations (48)-(52) to construct constraints that conform to the fault scenario: (48) (49) (50) (51) (52) In equations (48)-(52), and The square of the voltage at node i at time t and the square of the line current between node i and node j at time t, respectively; and They are respectively Timetable The active and reactive power transmitted upstream; and The lines are respectively Resistance and reactance; for Time Node With nodes Between lines The connected state; and They are respectively Timetable The active and reactive power transmitted upstream; and They are respectively The line between node j and node i at time point The active and reactive power transmitted upstream; and The lines are respectively Resistance and reactance; S7-2: Using equation (53), equation (16) is transformed into a second-order cone constraint: (53) S7-3: Modify equation (23) to construct power flow constraints using equation (54); (54) In equation (54), Represented as Time Node The square of the voltage at the auxiliary node aux; S7-4: Introduce auxiliary 0 / 1 variables and auxiliary voltage variables, and obtain the results using equations (55) and (56). Transformed constraints: (55) (56) In equation (55), For the line The maximum value at the OLTC tap position; S7-5: Constructing linearization constraints using equations (58) and (59): (58) (59) In equations (58) and (59), for Time corresponding node To the node On the line tap position The closed state; if closed, then The value is 1; if it is turned on, then... =0, for Time corresponding node To the node Tap position on the line The square of the voltage applied; S7-6: Using equation (60), the capacity constraint of R-SOP is transformed into a rotating cone constraint: (60)。 2. The multi-stage dynamic recovery method for a power distribution system considering cold load start-up characteristics according to claim 1, characterized in that, S2 includes the following steps: S2-1: Using equations (1)-(6), the operating model of the reconfigurable soft switch R-SOP is obtained: (1) (2) (3) (4) (5) (6) In equations (1)-(6), This represents the set of nodes connected to the voltage source converter (VSC). This represents the set of all voltage source converters; for Time Node Total loss of all connected VSCs The total DC-side active power of all VSCs, The total AC-side active power of all VSCs; for Time Node Apparent power transmitted via reconfigurable soft-switching R-SOP for Time Node Reactive power transmitted via reconfigurable soft switch R-SOP; for Time Node With voltage source converter The connected state; The operating loss factor for each voltage source converter; Voltage source converter The capacity; S2-2: Using equations (7)-(12), establish a fault reconfiguration model for a power distribution system containing a reconfigurable soft switch R-SOP: (7) (8) (9) (10) (11) (12) In equations (7)-(12), It is a set of distribution line nodes. For nodes of power distribution lines, ; Represents a node To the node The route, Represents all slave nodes To the node The route; It is a node With nodes Between lines The connected state; It is the number of nodes in the power distribution system; This refers to the number of substations in the power distribution system. It is the number of ports of the reconfigurable soft switch R-SOP; It is a node The on / off state of the connected reconfigurable soft switch R-SOP port, when R-SOP acts as a virtual power supply output and is positive. It equals 1, otherwise it equals 0; It is a line The virtual trend It is a line Virtual trends on the internet; yes Time Node The virtual current generated by the virtual power source; It is a node Virtual load demand; M is a constant; S2-3: Using equations (13)-(22), we obtain the fault flow model of the power distribution system containing reconfigurable soft switch R-SOP: (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) In equations (13)-(22), and The lines are respectively Resistance and reactance; for Timetable The current transmitted upwards; and They are respectively Time Node The injected active power and reactive power; , They are respectively Time Node , Voltage at the point; for Timetable The current transmitted upwards; and They are respectively Time Node The reduction in active power output of photovoltaic (PV) equipment and the reduction in active power output of photovoltaic equipment; and They are respectively Time Node The reduction in active power output of the wind turbine (Wind) and the reduction in active power output of the wind turbine; , They are Time Node The active and reactive power outputs of the distributed generation (DG); , for Time Node The active and reactive power outputs of the R-SOP; and They are respectively Time Node The reactive power output of photovoltaic (PV) equipment and wind turbine (Wind) is calculated. and They are respectively Time Node The active and reactive power consumed by load L; yes Time Node The reactive power output of the capacitor CBs can be switched on and off at the location; for Time Node The status of the load switch that controls the on / off state of the load; and These are the upper and lower limits of the node voltage in the power distribution system, respectively. This is the upper limit of the line current in the power distribution system.

3. The multi-stage dynamic recovery method for a power distribution system considering cold load start-up characteristics according to claim 2, characterized in that, S3 includes the following steps: S3-1: Establish the operating model of the on-load tap-changing transformer (OLTC) using equations (23) and (24): (23) (24) In equations (23)-(24), for Time Node The voltage at the auxiliary node aux is equal to the voltage on the secondary side of the on-load tap-changing transformer. for Timetable The tap position of the on-load tap-changing transformer (OLTC); for Timetable The voltage regulation rate of the on-load tap-changing transformer OLTC; For the line The initial voltage regulation rate of the on-load tap-changing transformer OLTC; For the line The change in voltage regulation at adjacent tap positions; A set of integer variables; S3-2: Using equations (25)-(28), construct the operation model of distributed generation (DG) and the operation model of switchable capacitor banks: (25) (26) (27) (28) In equations (25)-(28), , They are Time Node The active and reactive power outputs of the distributed generation (DG); for Time Node The distributed generation (DG) is in the on state; , These are the maximum active power output and maximum reactive power output of the distributed generation (DG), respectively. yes Time Node The reactive power output of the capacitor CBs can be switched on and off at the location; It refers to the capacitance of each group of switchable capacitors (CBs). yes Time Node The number of switchable capacitor banks that can be connected at a given location. This is the maximum number of switchable capacitor banks that can be switched on; S3-3: Construct the operating model of the Energy Storage System (ESS) using equations (29)-(33): (29) (30) (31) (32) (33) In equations (29)-(33), , These are the minimum and maximum charging power values ​​of the energy storage system (ESS), respectively. , These are the minimum and maximum discharge power of the energy storage system (ESS), respectively. for Auxiliary variables are set in real time, so that when the energy storage system (ESS) is charging, =1, when ESS discharges, let =0; , For example, the energy storage system ESS The charging power and discharging power at any given time; , , These represent the minimum, maximum, and initial values ​​of the energy storage state of charge, respectively. , These represent the total capacity of the energy storage system (ESS) and... The capacity of the ESS (Energy Storage System); for The capacity of the ESS (Energy Storage System); , These are the charging efficiency and discharging efficiency of the energy storage system (ESS), respectively. For time step.

4. The multi-stage dynamic recovery method for a power distribution system considering cold load start-up characteristics according to claim 3, characterized in that, S4 is the objective function used to establish the optimal load recovery stage model using equation (34). Equations (7)-(12), (13)-(22), (1), (2), (4)-(6), (33), and (23)-(32) are used as constraints for the optimal load recovery stage model. (34) In equation (34), , , These are, respectively, the operating losses of the power distribution system, the load reduction, and the reduction in renewable energy output. This is a weighting factor for the operating losses of the power distribution system. The weighting factor for load reduction. Weighting coefficients for the reduction in power output from new energy sources; This refers to the time of failure.

5. A multi-stage dynamic recovery method for a power distribution system considering cold load start-up characteristics according to claim 4, characterized in that, In S6, the objective function of the dynamic recovery stage model is established using equation (47), and equations (13)-(22), (42), (1), (2), (4)-(6), (33), (23)-(32), (43)-(46), and (35)-(41) are used as constraints of the dynamic recovery stage model: (47) In equation (47), It is the weighting coefficient for the energy deviation value of the two-stage energy storage.

6. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store programs that support the processor in executing the multi-stage dynamic recovery method for the power distribution system according to any one of claims 1-5, and the processor is configured to execute the programs stored in the memory.

7. A computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is run by the processor, it executes the steps of the multi-stage dynamic recovery method for the power distribution system according to any one of claims 1-5.

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