A multi-source cooperative active power distribution network recovery optimization method

Abstract

The application provides a multi-source cooperative active power distribution network recovery optimization method, the power distribution network comprises a plurality of load nodes and lines between the load nodes, each target load node in the plurality of load nodes is connected with a corresponding distributed power supply; first, an optimization model with a plurality of constraint conditions is established based on a preset typical fault scene set, taking the maximization of total power of the load nodes as the power distribution network recovery target, and then the column and constraint generation algorithm is used to iteratively solve the recovery optimization problem of the power distribution network through the optimization model, so as to obtain the final recovery strategy of the power distribution network. The application can realize multi-source cooperation and recovery strategy formulation of the power distribution network under extreme events, thereby alleviating the problems in the related art.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to a multi-source collaborative active distribution network restoration optimization method. Background Technology

[0002] The distribution network, located at the end of the power system, is most closely related to users. Ensuring its normal operation under extreme conditions is crucial for maintaining socio-economic stability and people's livelihoods, serving as a key link in the city's lifeline. However, the distribution network's disaster response capability is inferior to that of the transmission network, mainly due to: weaker power supply capacity; low level of automation in the current distribution network, incomplete remote control and automatic device configurations, and limited control methods; the inability of the conventional N-1 safe power supply criterion to meet the normal power supply conditions for users during large-scale multiple faults in the distribution network; and existing research on distribution network fault recovery and grid reconfiguration not being fully applicable to the needs of extreme events. Therefore, in-depth research on the recovery capability of the distribution network under extreme weather conditions has significant practical application value.

[0003] Most research on distribution network fault recovery focuses on the spatiotemporal connectivity advantages of multi-source coordination. Regarding distributed power sources, most studies only consider units with controllable output power, neglecting the impact of intermittent energy output uncertainty on the fault recovery process and strategy formulation. Furthermore, while there is considerable research on improving distribution network fault recovery capabilities using multi-source coordination, very few studies consider the coordination of multiple sources and the uncertainty of renewable energy output in extreme natural disaster scenarios, and the recovery strategies provided are mostly single-time-section strategies. Further research is needed on multi-source coordination and recovery strategy formulation for distribution networks under extreme events. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a multi-source collaborative active distribution network restoration optimization method to alleviate the above-mentioned problems existing in related technologies.

[0005] This invention provides a multi-source collaborative active distribution network restoration optimization method. The distribution network includes multiple load nodes and lines connecting these load nodes. Each target load node is connected to a corresponding distributed power source. The method includes: establishing an optimization model with multiple constraints based on a preset set of typical fault scenarios, with the goal of maximizing the total power output of the load nodes; iteratively solving the distribution network restoration optimization problem using a column and constraint generation algorithm through the optimization model to obtain the final restoration strategy of the distribution network; wherein the restoration strategy includes line power flow strategy, output strategy of each distributed power source, and switching strategy of each load node and each line. Each optimization involves solving the main optimization problem and sub-optimization problems sequentially through the optimization model based on the output of the distributed power source at that optimization time, and determining the restoration strategy for that optimization based on the solution results.

[0006] This invention provides a multi-source collaborative active distribution network restoration optimization method. The distribution network includes multiple load nodes and lines connecting these load nodes. Each target load node is connected to a corresponding distributed power source. First, an optimization model with multiple constraints is established based on a preset set of typical fault scenarios, with the goal of maximizing the total power consumption of the load nodes. Then, a column and constraint generation algorithm is used to iteratively solve the distribution network restoration optimization problem using the optimization model, thereby obtaining the final distribution network restoration strategy. Using this technique, multi-source collaboration and restoration strategy formulation for the distribution network under extreme events can be achieved, thus alleviating the problems existing in related technologies.

[0007] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained in accordance with the structures particularly pointed out in the description, claims and drawings.

[0008] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0009] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0010] Figure 1This is a flowchart illustrating a multi-source collaborative active distribution network recovery optimization method according to an embodiment of the present invention.

[0011] Figure 2 This is an example flowchart of the C&CG algorithm in an embodiment of the present invention;

[0012] Figure 3 This is a modified 62-node distribution network example diagram in an embodiment of the present invention;

[0013] Figure 4 This is an example diagram of the system information entropy probability distribution in an embodiment of the present invention;

[0014] Figure 5 This is an example diagram showing the recovery result of a five-fold fault scenario in an embodiment of the present invention;

[0015] Figure 6 This is an example diagram of the output curves of the distributed power source at different times in an embodiment of the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] Currently, most research on distribution network fault recovery focuses on the spatiotemporal connectivity advantages of multi-source coordination. Regarding distributed power sources, most studies only consider units with controllable output power, neglecting the impact of intermittent energy output uncertainty on the fault recovery process and strategy formulation. Furthermore, while there is considerable research on improving distribution network fault recovery capabilities using multi-source coordination, very few studies consider the coordination of multiple sources and the uncertainty of renewable energy output in extreme natural disaster scenarios. Moreover, the recovery strategies provided are mostly single-time-section-based. Further research is needed on multi-source coordination and recovery strategy formulation for distribution networks under extreme events.

[0018] Based on this, the present invention provides a multi-source collaborative active distribution network restoration optimization method, which can alleviate the above-mentioned problems existing in related technologies.

[0019] To facilitate understanding of this embodiment, a multi-source collaborative active distribution network restoration optimization method disclosed in this embodiment of the invention will be described in detail below.

[0020] A distribution network may include multiple load nodes and lines connecting these load nodes, with each target load node connected to a corresponding distributed power source; see also Figure 1 The diagram shows a flowchart of a multi-source collaborative active distribution network restoration optimization method, which may include the following steps:

[0021] Step S102: Based on a preset set of typical fault scenarios, establish an optimization model with multiple constraints that takes maximizing the total power of load nodes as the distribution network restoration objective.

[0022] The set of typical fault scenarios mentioned above can be determined based on the system information entropy of the distribution network under each fault scenario. This system information entropy characterizes the degree of uncertainty of the distribution network experiencing a fault.

[0023] For example, before performing the above step S102, the system information entropy of the distribution network under each fault scenario can be determined based on the fault rate of each line; then, the above typical fault scenario set can be determined based on the system information entropy of the distribution network under each fault scenario.

[0024] For example, during typhoon disasters, components of overhead power distribution lines are highly susceptible to damage and failure. To quickly reflect the impact of typhoon disasters and measure component failure rates with high accuracy, a typhoon wind field model can be used to calculate wind speeds at different locations during the typhoon, and a component failure probability model with a combined wind speed and direction distribution can be used to calculate the failure probability (i.e., failure rate) of a power distribution line under different wind speed and direction conditions.

[0025] For typhoon wind field models, the Rankine model, a numerical typhoon wind field model with relatively fast computation speed, can be selected. This wind field model can be described as follows:

[0026]

[0027] In equation (1): V p V is the wind speed at point p in the typhoon; eye For eye wind speed; R eye L is the radius of the eye of the storm. p Let p be the straight-line distance from point p in the typhoon to the center of the typhoon.

[0028] The specific formula for calculating the failure rate of a certain tower on a certain line of a distribution network can be:

[0029]

[0030] In equation (2), p T () represents the failure rate of the T-th tower contained in the n-th line; The failure rate of the T-th tower in the n-th line under normal operating conditions is represented by v; the real-time typhoon wind speed is v; θ is the angle between the typhoon wind direction and the line direction; v T The design wind speed that the T-th tower of the n-th line is designed to withstand; v T,max λ represents the maximum wind speed that the T-th tower within the n-th line can withstand, typically taken as twice the design wind speed; T This represents the sensitivity parameter of the typhoon to the T-th tower contained in the n-th line.

[0031] When the distribution network lines are equivalent to a series model, the formula for calculating the overall failure probability of a certain line in the distribution network can be:

[0032]

[0033] In equation (3), p line, k represents the failure rate of the nth line; T This represents the number of towers contained in the nth line.

[0034] Due to the large number of distribution network lines, listing all fault scenarios and incorporating them into the optimization scheme would severely impact the solution efficiency. Therefore, selecting typical fault scenarios is a crucial step in solving the optimization model. Extreme weather primarily affects distribution networks by significantly increasing component failure rates, leading to a higher probability of large-scale multiple faults. Given the numerous components in a distribution network, the number of multiple fault scenarios resulting from combinations of different faulty components is exceptionally large. However, not all scenarios are suitable for resilience assessment. Useful scenarios should possess a relatively high probability of occurrence and severe consequences. Therefore, it is necessary to select typical fault scenarios that extreme weather might cause for analysis based on the probability of occurrence and line failure rates. Typical fault scenarios can be determined based on the system information entropy of the distribution network under various fault scenarios; that is, reasonable system state scenarios are selected as typical fault scenarios based on the probability of a single fault event. Entropy is essentially a physical quantity representing the degree of inherent disorder in a system. In a power system, the distribution network can be considered an uncertain system where faults can occur at any moment, and entropy can represent the degree of uncertainty. The formula for calculating the system information entropy W of the distribution network under a certain resilience analysis scenario (i.e., a fault scenario) is as follows:

[0035]

[0036] In equation (4), Ω B p represents the set of all lines included in a distribution network. l This represents the failure rate of line l within the distribution network; z l z is a 0-1 variable characterizing whether a fault has occurred in line l of a distribution network. l=1 indicates that line l in the distribution network has a fault, z l =0 indicates that no fault has occurred in line l of the distribution network.

[0037] Each resilience analysis scenario corresponds to a z-axis consisting of the various lines within the distribution network. i The resulting vector z corresponds to the entropy value of the system in this scenario. l The value of p l Related to p l The higher the z-value, the more certain the line fault event is, and the more fault scenarios corresponding to z-values ​​there are. i The value is 1; when p i When z is 0, the uncertainty of the line fault event is infinite, and there must be a z-value in all fault scenarios. l The value is 0. Therefore, from the perspective of scenario selection, the system information entropy value of the distribution network under each resilience analysis scenario cannot be too large or too small, to ensure that the selected typical scenarios have the characteristics of high probability of occurrence and severe impact of fault consequences. The system information entropy value of the distribution network under each typical fault scenario must meet the following constraints:

[0038] W min ≤W≤W max (5)

[0039] Among them, W mim This represents the minimum system information entropy value of the distribution network under typical fault scenarios; W max This represents the maximum system information entropy value of the distribution network under typical fault scenarios.

[0040] Step S104: The distribution network recovery optimization problem is solved iteratively by using the column and constraint generation algorithm through the optimization model to obtain the final recovery strategy of the distribution network.

[0041] The recovery strategy mentioned above may include line power flow strategy, output strategy of each distributed power source, and switching strategy of each load node and each line. Each optimization is performed by solving the main optimization problem and sub-optimization problems in sequence according to the output of the distributed power source at that time, and the recovery strategy of that optimization is determined based on the solution results of that optimization.

[0042] This invention provides a multi-source collaborative active distribution network restoration optimization method. First, an optimization model with multiple constraints is established based on a preset set of typical fault scenarios, with the goal of maximizing the total power output of load nodes for distribution network restoration. Then, a column and constraint generation algorithm is used to iteratively solve the distribution network restoration optimization problem using the optimization model, thereby obtaining the final distribution network restoration strategy. Using this technique, multi-source collaboration and restoration strategy formulation for distribution networks under extreme events can be achieved, thus alleviating the problems existing in related technologies.

[0043] As one possible implementation, the above-mentioned multiple constraints may include: a first constraint characterizing the power balance of each load node after ignoring distribution network losses, a second constraint characterizing line power flow limitations, a third constraint characterizing the voltage limitations of each load node, a fourth constraint characterizing the output limitations of each distributed power source, a fifth constraint characterizing the radial topology of the power grid, and a sixth constraint characterizing the state changes of each load node.

[0044] In addition, considering the scenario of power grid restoration when multiple types of distributed power sources are connected to the power grid, the aforementioned distributed power sources may include at least one of energy storage devices, distributed wind turbines, and distributed photovoltaic units.

[0045] If the aforementioned distributed power source includes energy storage devices, the aforementioned multiple constraints may also include: an eighth constraint characterizing the charging and discharging power limit of the energy storage device, and a ninth constraint characterizing the charge limit of the energy storage device.

[0046] If the aforementioned distributed power sources include distributed wind turbines and / or distributed photovoltaic units, the plurality of constraints further include: a tenth constraint characterizing the output prediction error of distributed wind turbines and / or distributed photovoltaic units.

[0047] Based on the above constraints, step S102 (i.e., establishing an optimization model with multiple constraints based on a preset set of typical fault scenarios, with maximizing the total power of load nodes as the distribution network restoration objective) may include: establishing an objective function for the above distribution network restoration objective based on a preset set of typical fault scenarios; and establishing the above optimization model based on the above constraints and the objective function.

[0048] For ease of understanding, the above-mentioned constraints and the specific operation of step S102 are described as follows.

[0049] In the event of an extreme incident where the distribution network cannot obtain power support from the upstream grid, resulting in a complete substation outage, local distributed power sources within the distribution network can be used to supply power to critical loads. Traditional distribution network fault recovery typically involves only one distributed power source per electrical island. Multi-source coordination, as the name suggests, fully coordinates different types of local distributed power sources, utilizing undamaged lines and tie switches within the distribution network to connect them into the largest possible electrical island. The specific number of islands formed depends on the fault conditions within the distribution network; if two or more islands are formed, it must be ensured that each island is physically disconnected from the others.

[0050] Energy storage devices offer the advantage of stable output power, but their limited battery capacity prevents them from serving as the primary power source for distribution systems for extended periods. However, for distribution network fault recovery, the repair time for typically faulty equipment is not long; therefore, energy storage devices can be considered as short-term primary power sources during multi-source collaborative distribution network fault recovery. Energy storage devices must meet the following constraints:

[0051]

[0052]

[0053] α c +α d ≤1; α c ,α d ∈{0,1} (8)

[0054]

[0055]

[0056] In equations (6) to (10): The charging power for energy storage devices, α represents the discharge power of the energy storage device. c and α d α are binary variables representing the charging and discharging states of an energy storage device, respectively. c =1 and α d =0 indicates that the energy storage device is in a charging state, α c =0 and α d =1 indicates that the energy storage device is in a discharging state. Indicates the charging and discharging power limit of the energy storage device; This represents the charge of the energy storage device at time t; This refers to the minimum charge capacity of the energy storage device; This represents the maximum charge capacity of the energy storage device. η represents the initial charge of the energy storage device in the event of a fault. c η d Representing the charging efficiency and discharging efficiency of the energy storage device, respectively, η is assumed to be unaffected by the charging and discharging power. c η d All values ​​are taken as 0.9, and it is assumed that the reactive power compensation capacity of the energy storage device is sufficient; Δt is the operating time of the energy storage device.

[0057] Equations (6) and (7) represent the charging power limit and discharging power limit of the energy storage device, respectively; Equation (8) is used to control the charging and discharging state of the energy storage device; Equation (9) is the state of charge limit of the energy storage device; Equation (10) represents the energy charge of the energy storage device after a time interval Δt from the moment the energy storage device malfunctions. Based on this, equations (6) to (8) can be combined to form the eighth constraint condition to characterize the charging and discharging power limit of the energy storage device, and equations (9) and (10) can be combined to form the ninth constraint condition to characterize the energy charge limit of the energy storage device.

[0058] Wind turbines and solar PV units are uncontrollable distributed power sources. Their output is significantly affected by weather changes and exhibits considerable uncertainty. They cannot operate independently under load and must be combined with energy storage devices or controllable distributed power sources. Therefore, the distribution network can utilize a combined operation of energy storage and wind / solar power. For example, for a specific wind turbine or solar PV unit (i.e., an uncontrollable distributed unit), assuming the predicted output value P of this uncontrollable distributed unit has been obtained... i E,dg Based on this, the following uncertainty set is established to characterize the output prediction error of this uncontrollable distributed unit:

[0059]

[0060] In equation (11): For the actual output of load node i with uncontrollable distributed units, P represents the expected output of load node i with uncontrollable distributed units. i E,dg The prediction error between the actual minimum output and the predicted error. This represents the maximum actual output of load node i with uncontrollable distributed units and the expected output P. i E,dg The prediction error between them, P i E,dg - P i dg and Ψ represents the lower and upper limits of the active power output of load node i with uncontrollable distributed units, respectively. dg It is the set of load nodes consisting of all load nodes with uncontrollable distributed units.

[0061] Because using robust optimization to find the worst-case volatility criterion across the entire uncertainty set might lead to a conservative final strategy and risk missing the optimal solution, this issue can be addressed by using uncertainty cost to control the conservatism of the optimization model. The uncertainty set can then be parameterized with a volatility factor. and Auxiliary variable expression:

[0062]

[0063] In equation (12), the fluctuation factor corresponds to load node i with uncontrollable distributed units. and Standardized variables between [0,1] are used to describe the degree to which the output of the uncontrollable distributed generator deviates from the expected value upwards and downwards, respectively; N represents the uncertainty cost of the above optimization model, used to control... and The sum of the magnitudes, to better control the uncertainty. The global fluctuation range.

[0064] To better describe this, the robustness S of the above optimization model can also be defined as:

[0065]

[0066] In equation (13): n dg S represents the total number of uncontrollable distributed units. The value of S can vary from 0 to 1 to change the range of the uncertainty set and thus adjust the global conservatism of the uncertainty robust optimization. In particular, when S = 0, the uncertainty robust optimization is equivalent to deterministic optimization, and if S = 1, the uncertainty set represents the most uncertain case.

[0067] Assuming the uncontrollable distributed generator unit operates at a fixed power factor angle, the reactive power output of load node i with the uncontrollable distributed generator unit is... The representation can be: γ represents the power factor angle of the wind and solar turbine.

[0068]

[0069] In equation (14), γ represents the power factor angle of an uncontrollable distributed generator.

[0070] Equations (11) to (14) can be combined to form the tenth constraint condition mentioned above to characterize the output prediction error of distributed wind turbines and / or distributed photovoltaic units.

[0071] Since the primary objective of restoring the distribution network using distributed generation is to supply power to critical loads for as long as possible, the objective function for this distribution network restoration goal can be set as maximizing the total power restored to load nodes during the fault period. The formula for calculating the objective function for this distribution network restoration goal can be:

[0072]

[0073] Where f is the maximum total load power restored by the distribution network during the fault period; T is the total number of islanded operation periods of the distribution network; S is the set of typical fault scenarios; P s K represents the probability of a typical fault scenario occurring; Φ is the set of nodes consisting of all load nodes in the distribution network; i,t K is a binary variable characterizing whether load node i recovers within time period t. i,t =1 represents that load node i is re-energized within time period t, K i,t =0 indicates that load node i loses power during time period t; ω i,t The weighting coefficient representing the importance of load node i; P i,t Let be the active power of load node i during time period t.

[0074] The DistFlow power flow model is a commonly used method for calculating AC power flow in distribution networks. The DistFlow model uses the squares of active power, reactive power, and node voltages to represent the system state equations of the distribution network power system. The calculation formula for the DisFlow power flow model can be expressed as:

[0075]

[0076]

[0077]

[0078] In equations (16) to (18): Let t be the active power flowing from load node i to load node i+1 on line l, where load node i and load node i+1 are the starting and ending points of the line, respectively. Let t be the reactive power flowing from load node i to load node i+1 during time period t; and P represents the active power and reactive power flowing from load node i into load node i+1 on line l during time period t; i+1,t and Q i+1,t Let be the active power and reactive power of the load node i+1 itself during time period t, respectively. and Let r be the active power and reactive power provided by the distributed power source to load node i+1 during time period t; i x i These represent the resistance and reactance between load node i and load node i+1, respectively; V i,t For and V i+1,t Let be the voltages of load node i and load node i+1 during time period t, respectively. Since the losses in the distribution network lines are negligible, equations (16) to (18) can be linearized into the following form:

[0079]

[0080]

[0081]

[0082] In addition, the power flow of the line should also meet other operational constraints:

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] -(1-Z i,t M≤V i,t ≤(1-Z i,t M (27)

[0089]

[0090]

[0091] In the formula: P i,t and Q i,t Let be the active power and reactive power of load node i itself during time period t, respectively; and Let be the active power and reactive power provided by the distributed power source to load node i during time period t, respectively. and Z represents the maximum active and reactive power allowed to pass through line l, with load node i and load node i+1 as the starting and ending points of the line, respectively; i,t Z is a binary variable representing whether line l is connected. i,t =1 indicates that line l is connected, Z i,t =0 indicates that line l is disconnected; M is a very large constant; and These represent the maximum allowed active power output and maximum allowed maximum reactive power output of distributed power sources.

[0092] Equations (22) and (23) represent power balance constraints after ignoring distribution network line losses, Equations (24) and (25) represent line power flow constraints, Equations (26) and (27) represent load node voltage constraints, and Equations (28) and (29) represent distributed generation output constraints.

[0093] Equations (22) and (23) can be combined to form the first constraint condition to characterize the power balance of each load node after ignoring the distribution network loss. Equations (16) to (21), as well as (24) and (25), can be combined to form the second constraint condition to characterize the line power flow limitation. Equations (26) and (27) can be combined to form the third constraint condition to characterize the voltage limitation of each load node. Equations (28) and (29) can be combined to form the fourth constraint condition to characterize the output limitation of each distributed power source.

[0094] Distribution networks are characterized by closed-loop structures and open-loop operation. During restoration, the distribution network must maintain a radial structure at all times. Multi-source collaborative restoration schemes for distribution networks require coordinating as many distributed power sources as possible to form as large isolated islands as possible. Power source nodes and root nodes generally do not correspond, and single-product flow can lead to slow solutions to mixed-integer programming problems. Therefore, a radial structure constraint based on the "line disconnection and loop removal" approach can be adopted for the distribution network. The "line disconnection and loop removal" approach requires that the restored network generated by the optimization model should not contain any loops; therefore, all possible loops require at least one line to be disconnected. The radial constraint after line disconnection can be established as follows:

[0095]

[0096]

[0097]

[0098] In equations (30) to (32): C is the set of all "rings" in the recovery network; C k Let k be any "ring" (composed of multiple lines, which can be considered as a set of lines); z ij To characterize whether the line between load node i and load node j in ring "k" has been restored, z is a 0-1 variable. ij =1 indicates that the line between load node i and load node j has been restored, z ij =0 indicates that the line between load node i and load node j has not been restored; P is the set of lines consisting of all lines between root nodes in the restoration network; P k R1 represents line k in the recovery network; R2 represents the number of nodes in the recovery network; and R3 represents the number of root nodes in the recovery network.

[0099] Equation (30) means that for all possible "rings" in the recovery network, at least one line is disconnected to make them unconnected, that is, none of the possible "rings" in the recovery network are valid; Equation (31) means that for all possible lines between the root nodes in the recovery network, at least one line is disconnected to make them unconnected, that is, none of the root nodes in the recovery network are connected; Equation (32) means that the final number of lines and the number of nodes in the recovery network are related, that is, the number of edges (i.e. the number of lines) = the number of nodes - the number of root nodes.

[0100] Equations (30) to (32) can be combined to form the fifth constraint condition mentioned above to characterize the radial topology of the power grid.

[0101] During the power distribution network restoration process, it is essential to ensure that distributed generation sources continuously and stably supply power to critical load nodes. It is unacceptable for a load node to experience a sudden power outage after restoration. Therefore, it is necessary to impose constraints on the number of load node status changes.

[0102]

[0103] In equation (33), K i,t+1 K is a binary variable characterizing whether load node i recovers within time period t+1. i,t+1 =1 indicates that load node i is re-energized within time period t+1, K i,t+1 =0 indicates that load node i loses power during time period t+1.

[0104] Equation (33) indicates that each load node is only allowed to change its state once during the recovery process.

[0105] Equation (33) can be used as the sixth constraint condition to characterize the state changes of each load node.

[0106] As one possible implementation, the steps of iteratively solving the distribution network recovery optimization problem using the column and constraint generation algorithm may include: solving the main optimization problem based on the initial output strategy to obtain the initial total power of the load nodes and the initial switching strategy; and iteratively solving the sub-optimization problems and the main optimization problem based on the initial total power of the load nodes and the initial switching strategy to obtain the final recovery strategy of the distribution network.

[0107] For example, the steps of iteratively solving the optimization sub-problems and the optimization master problem based on the initial total load node power and the initial switching strategy to obtain the final recovery strategy of the distribution network may include: for the first optimization, solving the optimization sub-problems based on the initial switching strategy to obtain the output strategy and occurrence probability of this optimization, and solving the optimization master problem based on the output strategy of this optimization to obtain the switching strategy, line power flow strategy and total load node power for this optimization; for each optimization after the first optimization, solving the optimization sub-problems based on the switching strategy of the previous optimization to obtain the output strategy of this optimization, and solving the optimization master problem based on the output strategy of this optimization to obtain the switching strategy and line power flow strategy for this optimization; until the output strategy, switching strategy and line power flow strategy of two adjacent optimizations are the same, stopping the optimization and determining the output strategy, switching strategy and line power flow strategy of the last optimization as the final recovery strategy of the distribution network.

[0108] For ease of understanding, the steps of iteratively solving the distribution network restoration optimization problem using the column and constraint generation algorithm described above can be illustrated as follows.

[0109] In the above optimization model, equation (33) can be transformed into the following three-layer form:

[0110]

[0111] st Az≤b (35)

[0112] Bz≤d (36)

[0113] Cy≥Ez (37)

[0114] Dy=u (38)

[0115] Where: z=(K i,t ,z i,t ) represents the first-level optimization variable, indicating the switching strategy for each load node and each line; The second-level optimization variable represents the output strategy of each distributed power source, including the output fluctuation of wind turbines and / or photovoltaic units and the charging and discharging status of energy storage devices. The third-level optimization variable represents the power flow variable, including the load node recovery amount K. i,t *P i,t K i,t *Q i,t V i,t and the current state vector This represents the power flow strategy, where A, B, C, D, and E are parameter matrices representing each constraint in a compact form. T Let be the coefficient vector matrix of the objective function.

[0116] Equations (35) and (36) represent constraints related to changes in topology and load conditions, while equations (37) and (38) represent constraints related to line power flow balance and safe operation of the distribution network.

[0117] The above optimization model is a three-level optimization problem that cannot be solved directly using existing solvers. The column-and-constraint generation (C&CG) algorithm can be used to decouple the distribution network restoration optimization problem into a main optimization problem and an optimization subproblem. The processing scenario of the main optimization problem and the line switching strategy of the optimization subproblem are fixed respectively, and the solution is iterated repeatedly until the solution results of the main optimization problem and the optimization subproblem are equal.

[0118] The aforementioned optimization problem corresponds to the first stage decision-making process, in which the output strategy u of the distributed power source is given. * Since the output fluctuation of the main optimization problem is known, we replace the inner min-max problem with the variable η and add new constraints to obtain the relaxation problem of the main optimization problem. Therefore, the above main optimization problem is a mixed-integer linear programming problem with a single optimization objective, and its specific form is as follows:

[0119] maxη(39)

[0120] st η≤b T y (40)

[0121] Az≤b (41)

[0122] Bz≤d (42)

[0123] Cy≥Ez (43)

[0124] Dy=u * (44)

[0125] The above optimization subproblems assume that the load switching strategy and network topology are already determined, i.e., the optimal solution z of the relaxation master problem is known. * In this case, the output strategy u of each distributed power source is obtained. The specific form is as follows:

[0126]

[0127] st Cy≥Ez * (46)

[0128] Dy=u (47)

[0129] Solving equation (45) above is a two-layer optimization problem, which is not easy to solve numerically. The inner max problem is essentially a convex optimization problem. It can be dualized by introducing Lagrange multipliers Π1 and Π2 (both in vector form). The inner max problem is then transformed into a min problem and merged with the outer min problem to form a single min problem in the following form:

[0130]

[0131] st C T Π1+D T Π2=b (49)

[0132] Π1≤0, Π2unrestricted (50)

[0133]

[0134] Equation (51) is used to limit the number of units with uncertain output (such as wind turbines and photovoltaic units).

[0135] After transforming into a dual problem, u in the above objective function T Π2 terms have α i The form of multiplication with the dual variable is a non-convex optimization and must be handled. Therefore, the uncertainty cost N must be forced to be a positive integer. This means the worst-case volatility scenario will inevitably exist at the extreme point of the uncertainty interval, i.e., the volatility factor. and Transform the variable into a binary variable that is either 0 or 1, and then use the Big M method for relaxation:

[0136]

[0137] st C T П1+D T Π2=b (53)

[0138] h i ≤Π 2,i ,i∈Ψ dg (54)

[0139]

[0140] h i ≤Mα i (56)

[0141] h i ≥Π 2,i -M(1-α i (57)

[0142] hi ≥0 (58)

[0143] α i ∈{0,1}(59)

[0144] P E This is a vector representation of the expected output values ​​for all load nodes. Let h be the vector representation of the output prediction error of all load nodes; h is the vector introduced when transforming the max problem in the inner layer of equation (45) into the dual problem; h i The element in h corresponding to load node i; ∏ 2, It is the element in ∏2 corresponding to load node i.

[0145] After obtaining the relaxed main optimization problem and its subproblems, the C&CG algorithm needs to be iteratively executed to solve them. For example... Figure 2 As shown, the specific process of the C&CG algorithm mainly includes:

[0146] Step 1: Let the lower bound LB = -∞, the upper bound UB = +∞, and the convergence criterion ε = 10. -5 .

[0147] Step 2: Set the uncontrollable distributed unit volatility factor in the main problem (i.e., the optimization main problem) to 0, and obtain the switching strategy z. * Find the optimal value η, and update the upper bound UB = min{UB,η}.

[0148] Step 3, set the iteration count k = 1.

[0149] Step 4: Let z be the cutting strategy of the subproblem (i.e., the optimization subproblem) in the k-th iteration. k =z * Solve for the output strategy u * Find the optimal solution Ps, and update the lower bound LB = max{LB, Ps}.

[0150] Step 5, let u be the output strategy of the main problem in the k-th iteration. k =u * Solve for the switching strategy z * The power flow variable y at the kth iteration k Find the optimal value η, and update the upper bound UB = min{UB,η}.

[0151] Step 6: Determine if |UB-LB|≤ε is satisfied; if |UB-LB|≤ε is satisfied, then return Ps and z. k u k y k The process ends; if |UB-LB|≤ε is satisfied, then set the iteration count k=k+1 and return to step 4.

[0152] To further verify the effectiveness of the above-mentioned multi-source collaborative active distribution network restoration optimization method, an experiment is conducted using a specific example as follows:

[0153] A modified 62-node distribution network in a certain region is used as a case study for analysis. For example... Figure 3 As shown, this example includes busbars from three 10kV substations and 59 load nodes. Five primary load nodes, eight secondary load nodes, and all remaining nodes are tertiary load nodes. The importance classification of each load node is shown in Table 2, and the initial weight coefficient ratio for each load node level is 100:10:1. To verify the performance of the above optimization model, a gas turbine was added to load node 33, a diesel generator to load node 40, energy storage devices to load nodes 22, 25, and 53, and wind turbines to load nodes 38, 48, and 52. The parameters of each distributed power source are shown in Table 1. In addition, all primary load nodes are equipped with emergency power supplies with a capacity 1.1 times the capacity and a backup time of 2 hours, and all secondary loads are equipped with emergency power supplies with a capacity 1.1 times the capacity and a backup time of 1 hour. Assume the coordinates of load node 1 are (0,0), the initial landfall location of the typhoon is (-80km,-80km), the center of the typhoon passes through the power distribution network at a speed of 20km / h along the trajectory of y=x in the coordinate system, and the initial central pressure of the typhoon is 925hpa.

[0154] Table 1 Distributed Power Supply Parameters

[0155]

[0156] Multiple fault scenarios are generated by setting the fault deduplication number based on the fault rate of each line, and the system information entropy value of the distribution network under these fault scenarios is calculated. The probability of a single fault scenario occurring can be calculated from the fault rate of each line within the scenario. The system information entropy value of the distribution network under these fault scenarios conforms to... Figure 4 The probability distribution shown is Figure 4 Most of the system information entropy values ​​are distributed within the interval [5, 20]. Therefore, fault scenarios with system information entropy values ​​within the interval [5, 20] can be selected as typical fault scenarios with relatively high probability of occurrence and serious consequences to form a typical fault scenario set. Taking one typical fault scenario as an example, in this typical fault scenario, lines 22, 23, 41, 42, and 53 are in a fault state, with corresponding fault rates of 0.3155, 0.3157, 0.3122, 0.9969, and 0.3123, respectively. At this time, the system information entropy value of the distribution network is 8.3651, which belongs to the extreme fault scenario under typhoon weather. The fault lines under some typical fault scenarios are shown in Table 3.

[0157] Table 2 Classification of Importance Levels of Load Nodes

[0158]

[0159] Table 3 shows the faulty circuits under some typical fault scenarios.

[0160]

[0161] Assume that after the power distribution network is impacted by a typhoon, all busbars 1, 23, and 43 from the substation lose power, with an estimated outage time of 10 hours. Dividing the outage into 1-hour periods, and taking a typical five-fold fault scenario as an example, lines 4-5, 8-9, 15-16, 30-31, and 51-52 are in an unrecoverable state. In the first 2 hours of the outage, the emergency backup power supply provides power to secondary loads for 1 hour and primary loads for 2 hours. Once the emergency backup power supply is exhausted, distributed power sources will provide power. The final recovery result is as follows... Figure 5 As shown, a total of 5 primary load nodes, 7 secondary load nodes, and 24 tertiary load nodes were restored. The restoration rate of primary load nodes was 100%, that of secondary load nodes was 87.5%, and that of tertiary load nodes was 47.83%. Primary load nodes 12, 33, 40, and 57 were jointly powered by the nearest distributed power source and energy storage device. Due to the damage to lines 4-5, the critical primary load at node 18 could not be powered by the nearest energy storage device ESS1; therefore, it was jointly powered by energy storage device ESS2 and a gas turbine via tie switches 17-29. The restoration target required the formation of only one large island. Given the limited energy of the distributed power source and the damage to lines 51-52, secondary load node 51 was not restored, and the wind turbine at tertiary load node 52 could not be put into operation. The output results of the remaining distributed power sources at various times are shown in the figure. Figure 6 This paper restores the above five fault scenarios using the multi-source collaborative active distribution network restoration optimization method. The occurrence probability and load restoration status of all fault scenarios in the typical fault scenario set are calculated respectively. The results show that under the typhoon weather conditions set in this example, the restoration strategy formulated based on the multi-source collaborative approach can ensure that an average of about 55.97% of the load nodes continue to supply power during the fault time, facing all possible typical fault scenarios.

[0162] Unless otherwise specifically stated, the relative steps, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention.

[0163] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0164] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0165] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A multi-source collaborative active distribution network restoration optimization method, characterized in that, The power distribution network includes multiple load nodes and lines connecting these load nodes, and each target load node among the multiple load nodes is connected to a corresponding distributed power source; the method includes: Based on the failure rate of each line, the system information entropy of the distribution network under each failure scenario is determined; wherein, the system information entropy characterizes the degree of uncertainty of the distribution network experiencing a failure. Based on the system information entropy of the power distribution network under various fault scenarios, a set of typical fault scenarios is determined. Based on the set of typical fault scenarios, and taking maximizing the total power consumption of load nodes as the distribution network restoration objective, an objective function is established for the distribution network restoration objective according to the following formula: in, This represents the maximum total load that the distribution network can restore during the fault period. This represents the total number of time periods during which the distribution network operates in islanded mode. A collection of typical fault scenarios; This represents the probability of a typical failure scenario occurring. Φ It is the set of nodes consisting of all load nodes in the distribution network; To characterize load nodes During the period Whether the internal binary variable is restored Characterizing load nodes During the period Internal power restoration Characterizing load nodes During the period Internal power loss; To characterize load nodes The weighting coefficients for the degree of importance; For load nodes During the period Active power within; Based on multiple constraints and the objective function, an optimization model with the multiple constraints is established, which takes maximizing the total power of load nodes as the distribution network recovery objective. The multiple constraints include: a first constraint characterizing the power balance of each load node after ignoring distribution network losses; a second constraint characterizing line power flow limitations; a third constraint characterizing the voltage limitations of each load node; a fourth constraint characterizing the output limitations of each distributed power source; a fifth constraint characterizing the radial topology of the power grid; and a sixth constraint characterizing the state changes of each load node. The optimization model employs a column and constraint generation algorithm to iteratively solve the distribution network recovery optimization problem, thereby obtaining the final recovery strategy for the distribution network. The recovery strategy includes line power flow strategy, output strategy of each distributed power source, and switching strategy of each load node and each line. Each optimization is performed by solving the main optimization problem and sub-optimization problems sequentially based on the output of the distributed power sources at that time, and the recovery strategy for that optimization is determined based on the solution results.

2. The method according to claim 1, characterized in that, The distributed power source includes at least one of the following: energy storage equipment, distributed wind turbine, and distributed photovoltaic unit.

3. The method according to claim 2, characterized in that, The distributed power source includes an energy storage device, and the multiple constraints further include: an eighth constraint characterizing the charging and discharging power limit of the energy storage device, and a ninth constraint characterizing the charge limit of the energy storage device.

4. The method according to claim 2, characterized in that, The distributed power source includes distributed wind turbines and / or distributed photovoltaic units, and the multiple constraints also include a tenth constraint characterizing the output prediction error of distributed wind turbines and / or distributed photovoltaic units.

5. The method according to any one of claims 1-4, characterized in that, The steps for iteratively solving the distribution network restoration optimization problem using a column and constraint generation algorithm include: The optimization master problem is solved based on the initial output strategy to obtain the initial total power of the load nodes and the initial switching strategy. Based on the initial total power of the load nodes and the initial switching strategy, the optimization sub-problem and the optimization master problem are solved iteratively to obtain the final recovery strategy of the distribution network.

6. The method according to claim 5, characterized in that, Based on the initial total power of the load nodes and the initial switching strategy, the steps of iteratively solving the optimization sub-problem and the optimization master problem to obtain the final recovery strategy of the distribution network include: For the first optimization, the optimization sub-problem is solved based on the initial switching strategy to obtain the output strategy and occurrence probability of this optimization, and the optimization master problem is solved based on the output strategy of this optimization to obtain the switching strategy, line power flow strategy and total load node power of this optimization. For each subsequent optimization, the optimization sub-problem is solved based on the previous optimization switching strategy to obtain the output strategy for this optimization, and the optimization master problem is solved based on the output strategy for this optimization to obtain the switching strategy and line power flow strategy for this optimization. Optimization stops when the output strategy, switching strategy, and line power flow strategy are identical in two consecutive optimizations, and the output strategy, switching strategy, and line power flow strategy of the last optimization are determined as the final recovery strategy for the distribution network.

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