Micro-grid black start recovery optimization method and device based on adaptive Benders decomposition

Abstract

The invention provides a micro-grid black start recovery optimization method and device based on adaptive Benders decomposition, and the method comprises the steps: providing a Benders two-stage solving algorithm fused with an adaptive penalty factor for the hierarchy and constraint complexity of a micro-grid black start two-stage optimization model. In the first optimization stage, a micro-source recovery sequence and a recovery path are optimized based on a Benders decomposition method of an adaptive penalty factor, and in the second optimization stage, load recovery is optimized in combination with mixed integer programming. According to the method, the precision of the optical storage model is improved through dynamic characteristic correction, the recovery efficiency and stability are balanced through a two-stage framework, the solving performance is improved through an adaptive algorithm, and efficient and safe recovery of black start of the micro-grid is effectively achieved.

Description

Technical Field

[0001] This invention relates to the field of microgrid black-start recovery technology, and in particular to a microgrid black-start recovery optimization method and apparatus based on adaptive Benders decomposition. Background Technology

[0002] With the large-scale integration of distributed power sources, the power system's operational structure is becoming increasingly complex, increasing the risk of major blackouts. Microgrids, as an important auxiliary means for power system black-start recovery, have reduced disturbance resistance when operating in isolated grids without the support of the main grid, making them prone to entering a "complete blackout" state. Existing technologies have the following shortcomings: they do not fully consider the volatility of photovoltaic output and the dynamic response characteristics of energy storage; the selection criteria for nodes and lines are one-sided, failing to comprehensively consider topological and electrical attributes; and they mostly focus on a single stage of micro-source or load recovery, making it difficult to find the overall optimal solution. Summary of the Invention

[0003] In view of this, the present invention provides a microgrid black-start recovery optimization method based on adaptive Benders decomposition. One or more embodiments of this specification also relate to a microgrid black-start recovery optimization device based on adaptive Benders decomposition, a computing device, a computer-readable storage medium, and a computer program, to address the technical deficiencies existing in the prior art.

[0004] According to a first aspect of the present invention, a microgrid black-start recovery optimization method based on adaptive Benders decomposition is provided, comprising: Obtain comprehensive power parameters of the power system to be restored, and determine the power supply of all nodes in the power system to be restored according to two preset optimization stages; The first optimization stage includes: determining the restoration order of multiple target micro-source nodes in the power system to be restored based on comprehensive power parameters and a two-level programming model constructed using the Benders decomposition method with adaptive adjustment of penalty factors; determining the restoration path based on the restoration order; and generating a first power supply topology including the target micro-source nodes. The two-level programming model includes an upper-level programming model for determining the restoration order and a lower-level programming model for determining the restoration path. The target micro-source nodes include photovoltaic nodes, energy storage nodes, and key load nodes. The second optimization stage includes: based on the comprehensive power parameters and the first power supply topology, combined with the preset optimization model, determining the restoration order and restoration path of the remaining nodes in the power system to be restored, and obtaining the second power supply topology including all nodes, wherein the remaining nodes are nodes other than the target micro source; Power restoration is performed on the power system to be restored according to the second power supply topology.

[0005] In some implementations, the upper-level planning model includes:

[0006] in, This represents the maximum value of the upper-level planning model during multiple iterations. This represents the amount of load restoration within the energized area of ​​Phase 1; This is the load recovery adjustment coefficient, used to characterize the degree of recovery of the out-of-power load; These are auxiliary variables for lower-level planning, used to integrate lower-level constraints; This represents the integral sum of available photovoltaic active power output during the black start recovery process of a microgrid. This represents the integral sum of the available active power output of the energy storage system during the black start recovery process of a microgrid. This is a penalty factor.

[0007] In some implementations, the step of calculating the integral sum of available photovoltaic active power output during the microgrid black-start recovery process includes: Based on comprehensive power parameters, the photovoltaic output at each time step is calculated; Based on the photovoltaic output at each time step, the integral sum of the available photovoltaic active power output is calculated. The constraint expressions for calculating the photovoltaic output at each time step include:

[0008] in, It is a collection of distributed photovoltaic systems within a microgrid; This refers to the operating status of distributed photovoltaic (PV) systems. For the active power output of distributed photovoltaic r in the t-th time step, Let r be the reactive power output of the distributed photovoltaic system in the t-th time step; Let r be the predicted active power value of the distributed photovoltaic system at time step t. Let r be the predicted reactive power output of the distributed photovoltaic system at the t-th time step.

[0009] In some implementations, the step of calculating the predicted active power of photovoltaic power includes: Based on comprehensive power parameters, the dynamic starting power correction coefficient is calculated, and the corresponding calculation formula includes:

[0010]

[0011] in, The reference correction factor (range 0.8~0.9) is used under standard test conditions (illuminance G0=1000W / m2, component temperature T0=25℃). The light intensity factor reflects the compensation requirement for starting power when there is insufficient light. =0.3~0.5 is the light sensitivity coefficient, and G(t) is the actual light intensity at time t; Temperature influence factor ( ), reflecting the correction of starting power caused by the decrease in component efficiency at high temperatures; kT is the temperature coefficient (range -0.002~0.004℃). Let t be the component temperature at time step t; If photovoltaic power is a black-start power source, the available active power output is: , in, This represents the predicted maximum photovoltaic output at time step t. If the photovoltaic system is a non-self-starting micro-source, the usable active power output is:

[0012] in, This is the baseline value for starting power under standard conditions; This is the corrected actual starting power; To initiate the start step, To complete the step.

[0013] In some implementations, the step of calculating the integral sum of the available active power output of energy storage during the microgrid black-start recovery process includes: Based on comprehensive power parameters, calculate the energy storage output at each time step; Based on the energy storage output at each time step, calculate the integral sum of the available active power output of the energy storage. The constraint expressions for calculating the energy storage output at each time step include:

[0014] in, A collection of energy storage devices within a microgrid; This refers to the operating state of the energy storage device s; The charging state of the energy storage device s This represents the discharge state of the energy storage device s; The charging power of energy storage device s in the t-th time step, Let be the discharge power of energy storage device s in the t-th time step; The minimum charging power of the energy storage device s, The maximum charging power of the energy storage device s; The minimum discharge power of the energy storage device s, denoted as s, representing the maximum discharge power of the energy storage device.

[0015] In some implementations, the step of calculating the active power prediction value of energy storage includes: Based on comprehensive power parameters, the dynamic discharge efficiency is calculated, and the corresponding formulas include:

[0016] in, The energy storage discharge efficiency varies with the remaining energy (state of charge (SOC(t))) and the number of charge-discharge cycles. Dynamic correction; The baseline discharge efficiency under standard conditions for the new equipment (values ​​range from 0.9 to 0.95); h(SOC(t)) is the residual energy influence factor; This represents the remaining energy at time step t. This represents the maximum energy storage capacity. The number of cycles is the influencing factor; Ncyc is the cumulative number of charge-discharge cycles, and each complete charge-discharge cycle is counted as one cycle; Based on the calculated dynamic discharge efficiency, the formula for calculating the corrected energy storage output includes:

[0017] in, This represents the maximum discharge power of the energy storage. Minimum capacity limit; The time step length.

[0018] In some implementations, the lower-level planning model includes:

[0019] in, This represents the maximum value of the lower-level planning model during multiple iterations. Let be the importance of the i-th node. Let be the line weight of the j-th line.

[0020] In some implementations, the formula for calculating node importance includes:

[0021] in, The normalized node degree (reflecting topological connectivity) is defined as the ratio of the number of connections a node has to the maximum node degree in the entire network. The normalized load contribution is the ratio of the load power carried by a node to the load power of the largest node in the entire network. The normalized load level contribution is obtained by standardizing the load level weights connected to the node (Level 1 load 1.0, Level 2 load 0.2, Level 3 load 0.01). For node degree, Contribution to node load Weighting coefficients for the contribution of load level.

[0022] In some implementations, the formula for calculating the line weights includes:

[0023] in, This is the normalized path betweenness (reflecting topological criticality), which is the percentage of frequency that path j appears in the shortest paths of the entire network; The normalized line charging capacitor (reflecting overvoltage risk) has a higher weighting value for the larger the capacitor. The normalized line recovery time (reflecting operational efficiency) has a higher weighting for longer recovery times. , and These are the weighting coefficients for line side betweenness, line charging capacitance, and line recovery time, respectively.

[0024] In some implementations, the optimization model for the second optimization stage includes:

[0025] In the formula, This marks the end of the first phase. The duration of the second phase; Let be the total active power of the load that has been restored at time t; Let be the active power of the restored load at node i. The set of loads that have been restored at time t; Importance-weighted power for restored loads. Let be the weight of the i-th node; and Weighting coefficients ( , usually take , These figures respectively reflect the emphasis on the amount of recovery and its importance.

[0026] According to a second aspect of the present invention, a microgrid black-start recovery optimization device based on adaptive Benders decomposition is provided, comprising: The acquisition module is used to acquire the comprehensive power parameters of the power system to be restored, and determine the power supply of all nodes in the power system to be restored according to two preset optimization stages; The first optimization module includes: determining the restoration order of multiple target micro-source nodes in the power system to be restored based on comprehensive power parameters and a two-level programming model constructed using the Benders decomposition method with adaptive adjustment of penalty factors; determining the restoration path based on the restoration order; and generating a first power supply topology including the target micro-source nodes. The two-level programming model includes an upper-level programming model for determining the restoration order and a lower-level programming model for determining the restoration path. The target micro-source nodes include photovoltaic nodes, energy storage nodes, and key load nodes. The second optimization module is used to: determine the restoration order and restoration path of the remaining nodes in the power system to be restored based on the comprehensive power parameters and the first power supply topology, combined with a preset optimization model, to obtain a second power supply topology that includes all nodes, wherein the remaining nodes are nodes other than the target micro source; The recovery module is used to restore power to the power system to be restored according to the second power supply topology.

[0027] In some implementations, the upper-level planning model includes:

[0028] in, This represents the maximum value of the upper-level planning model during multiple iterations. This represents the amount of load restoration within the energized area of ​​Phase 1; This is the load recovery adjustment coefficient, used to characterize the degree of recovery of the out-of-power load; These are auxiliary variables for lower-level planning, used to integrate lower-level constraints; This represents the integral sum of available photovoltaic active power output during the black start recovery process of a microgrid. This represents the integral sum of the available active power output of the energy storage system during the black start recovery process of a microgrid. This is a penalty factor.

[0029] In some implementations, the step of calculating the integral sum of available photovoltaic active power output during the microgrid black-start recovery process includes: Based on comprehensive power parameters, the photovoltaic output at each time step is calculated; Based on the photovoltaic output at each time step, the integral sum of the available photovoltaic active power output is calculated. The constraint expressions for calculating the photovoltaic output at each time step include:

[0030] in, It is a collection of distributed photovoltaic systems within a microgrid; This refers to the operating status of distributed photovoltaic (PV) systems. For the active power output of distributed photovoltaic r in the t-th time step, Let r be the reactive power output of the distributed photovoltaic system in the t-th time step; Let r be the predicted active power value of the distributed photovoltaic system at time step t. Let r be the predicted reactive power output of the distributed photovoltaic system at the t-th time step.

[0031] In some implementations, the step of calculating the predicted active power of photovoltaic power includes: Based on comprehensive power parameters, the dynamic starting power correction coefficient is calculated, and the corresponding calculation formula includes:

[0032]

[0033] in, The reference correction factor (range 0.8~0.9) is used under standard test conditions (illuminance G0=1000W / m2, component temperature T0=25℃). The light intensity factor reflects the compensation requirement for starting power when there is insufficient light. =0.3~0.5 is the light sensitivity coefficient, and G(t) is the actual light intensity at time t; Temperature influence factor ( ), reflecting the correction of starting power caused by the decrease in component efficiency at high temperatures; kT is the temperature coefficient (range -0.002~0.004℃). Let t be the component temperature at time step t; If photovoltaic power is a black-start power source, the available active power output is: , in, This is the predicted maximum photovoltaic output at time step t.

[0034] If the photovoltaic system is a non-self-starting micro-source, the usable active power output is:

[0035] in, This is the baseline value for starting power under standard conditions; This is the corrected actual starting power; To initiate the start step, To complete the step.

[0036] In some implementations, the step of calculating the integral sum of the available active power output of energy storage during the microgrid black-start recovery process includes: Based on comprehensive power parameters, calculate the energy storage output at each time step; Based on the energy storage output at each time step, calculate the integral sum of the available active power output of the energy storage. The constraint expressions for calculating the energy storage output at each time step include:

[0037] in, A collection of energy storage devices within a microgrid; This refers to the operating state of the energy storage device s; The charging state of the energy storage device s This represents the discharge state of the energy storage device s; The charging power of energy storage device s in the t-th time step, Let be the discharge power of energy storage device s in the t-th time step; The minimum charging power of the energy storage device s, The maximum charging power of the energy storage device s; The minimum discharge power of the energy storage device s, denoted as s, representing the maximum discharge power of the energy storage device.

[0038] In some implementations, the step of calculating the active power prediction value of energy storage includes: Based on comprehensive power parameters, the dynamic discharge efficiency is calculated, and the corresponding formulas include:

[0039] in, The energy storage discharge efficiency varies with the remaining energy (state of charge (SOC(t))) and the number of charge-discharge cycles. Dynamic correction; The baseline discharge efficiency under standard conditions for the new equipment (values ​​range from 0.9 to 0.95); h(SOC(t)) is the residual energy influence factor; This represents the remaining energy at time step t. This represents the maximum energy storage capacity. The number of cycles is the influencing factor; Ncyc is the cumulative number of charge-discharge cycles, and each complete charge-discharge cycle is counted as one cycle; Based on the calculated dynamic discharge efficiency, the formula for calculating the corrected energy storage output includes:

[0040] in, This represents the maximum discharge power of the energy storage. Minimum capacity limit; The time step length.

[0041] In some implementations, the lower-level planning model includes:

[0042] in, This represents the maximum value of the lower-level planning model during multiple iterations. Let be the importance of the i-th node. Let be the line weight of the j-th line.

[0043] In some implementations, the formula for calculating node importance includes:

[0044] in, The normalized node degree (reflecting topological connectivity) is defined as the ratio of the number of connections a node has to the maximum node degree in the entire network. The normalized load contribution is the ratio of the load power carried by a node to the load power of the largest node in the entire network. The normalized load level contribution is obtained by standardizing the load level weights connected to the node (Level 1 load 1.0, Level 2 load 0.2, Level 3 load 0.01). For node degree, Contribution to node load Weighting coefficients for the contribution of load level.

[0045] In some implementations, the formula for calculating the line weights includes:

[0046] in, This is the normalized path betweenness (reflecting topological criticality), which is the percentage of frequency that path j appears in the shortest paths of the entire network; The normalized line charging capacitor (reflecting overvoltage risk) has a higher weighting value for the larger the capacitor. The normalized line recovery time (reflecting operational efficiency) has a higher weighting for longer recovery times. , and These are the weighting coefficients for line side betweenness, line charging capacitance, and line recovery time, respectively.

[0047] In some implementations, the optimization model for the second optimization stage includes:

[0048] In the formula, This marks the end of the first phase. The duration of the second phase; Let be the total active power of the load that has been restored at time t; Let be the active power of the restored load at node i. The set of loads that have been restored at time t; Importance-weighted power for restored loads. Let be the weight of the i-th node; and Weighting coefficients ( , usually take , These figures respectively reflect the emphasis on the amount of recovery and its importance.

[0049] According to a third aspect of the present invention, a computing device is provided, comprising: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of the microgrid black-start recovery optimization method based on adaptive Benders decomposition.

[0050] According to a fourth aspect of the present invention, a computer-readable storage medium is provided storing computer-executable instructions that, when executed by a processor, implement the steps of the above-described microgrid black-start recovery optimization method based on adaptive Benders decomposition.

[0051] According to a fifth aspect of the present invention, a computer program is provided, wherein when the computer program is executed in a computer, the computer is instructed to perform the steps of the microgrid black-start recovery optimization method based on adaptive Benders decomposition described above.

[0052] At least one embodiment of this invention proposes a Benders two-stage solution algorithm incorporating an adaptive penalty factor to address the hierarchical and constraint complexity of the two-stage optimization model for microgrid black start. The first optimization stage optimizes the micro-source recovery sequence and path based on the Benders decomposition method with an adaptive penalty factor. The second optimization stage combines mixed-integer programming to optimize load recovery. This invention improves the accuracy of the photovoltaic-storage model through dynamic characteristic correction, balances recovery efficiency and stability through a two-stage framework, and enhances solution performance through an adaptive algorithm, effectively achieving efficient and safe recovery from microgrid black start. Attached Figure Description

[0053] Figure 1 This is a flowchart of a microgrid black-start recovery optimization method based on adaptive Benders decomposition provided by the present invention; Figure 2 This invention provides a structural block diagram of a microgrid black-start recovery optimization method based on adaptive Benders decomposition and dynamic characteristic correction. Figure 3 The flowchart of the Benders decomposition method with fused adaptive penalty factor is provided by the present invention for a microgrid black start recovery optimization method based on adaptive Benders decomposition and dynamic characteristic correction. Figure 4This invention provides a microgrid topology based on an adaptive Benders decomposition and dynamic characteristic correction-based microgrid black-start recovery optimization method. Figure 5 This is a simplified structural diagram of a microgrid black-start recovery optimization device based on adaptive Benders decomposition provided by the present invention; Figure 6 This is a structural block diagram of a computing device provided by the present invention. Detailed Implementation

[0054] Many specific details are set forth in the following description to provide a full understanding of this specification. However, this specification can be implemented in many other ways than those described herein, and those skilled in the art can make similar extensions without departing from the spirit of this specification. Therefore, this specification is not limited to the specific implementations disclosed below.

[0055] The terminology used in one or more embodiments of this specification is for the purpose of describing particular embodiments only and is not intended to limit the scope of the one or more embodiments of this specification. The singular forms “a” and “the” as used in one or more embodiments of this specification and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in one or more embodiments of this specification refers to and includes any or all possible combinations of one or more associated listed items. The modifications “a” and “a plurality” as used in this disclosure are illustrative and not restrictive, and those skilled in the art will understand that they should be understood as “one or more” unless the context clearly indicates otherwise.

[0056] It should be understood that although the terms first, second, etc., may be used to describe various information in one or more embodiments of this specification, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, first may also be referred to as second without departing from the scope of one or more embodiments of this specification, and similarly, second may also be referred to as first. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to a determination."

[0057] See Figure 1 , Figure 1 A flowchart of a microgrid black-start recovery optimization method based on adaptive Benders decomposition, according to some embodiments of this specification, is shown, specifically including the following steps.

[0058] Step 101: Obtain the comprehensive power parameters of the power system to be restored, and determine the power supply of all nodes in the power system to be restored according to the two preset optimization stages.

[0059] In some embodiments, the execution entity (such as a pre-defined computing device) of the microgrid black-start recovery optimization method based on adaptive Benders decomposition can be connected to the target device via a wired or wireless connection. The aforementioned wireless connection methods may include, but are not limited to, 3G / 4G / 5G / 6G connections, WiFi connections, Bluetooth connections, WiMAX connections, Zigbee connections, UWB (ultra-wideband) connections, and other currently known or future-developed wireless connection methods.

[0060] Comprehensive power parameters can refer to a multi-dimensional data set that reflects the operating status of the power grid. For example, the execution method includes collecting real-time measurement data such as voltage, current, frequency, and power factor, as well as environmental parameters such as light intensity and component temperature, to provide dynamic input basis for subsequent calculations.

[0061] Step 102: The first optimization stage includes: determining the recovery order of multiple target micro-source nodes in the power system to be restored based on the comprehensive power parameters and a two-level programming model constructed using the Benders decomposition method with adaptive adjustment of penalty factors; determining the recovery path based on the recovery order; and generating a first power supply topology including the target micro-source nodes. The two-level programming model includes an upper-level programming model for determining the recovery order and a lower-level programming model for determining the recovery path. The target micro-source nodes include photovoltaic nodes, energy storage nodes, and key load nodes.

[0062] A two-layer programming model can refer to a nested optimization framework. For example, the upper layer generates a recovery sequence scheme and passes it to the lower layer for path verification. A two-way feedback mechanism ensures the feasibility of the solution, balancing the global and local feasibility of the decision. In the micro-source recovery two-layer model established in this invention, the upper-layer model aims to maximize the available active power output of the microgrid while restoring the load in the already energized area. Considering the recovery characteristics and output constraints of photovoltaic and energy storage, it optimizes the recovery time of non-self-starting micro-sources and uses the Benders decomposition method with an adaptive penalty factor to pass the micro-source recovery sequence to the lower layer. The lower layer, based on the recovery sequence given by the upper layer, searches for the optimal recovery path of the micro-sources and returns the grid recovery status to the upper layer. At this point, the upper-layer model uses the grid recovery status as a new constraint to generate a new recovery sequence and pass it to the lower layer. This process is repeated until the conditions of both the upper and lower layer constraints are met, obtaining the optimal micro-source recovery scheme.

[0063] Target micro-source nodes can refer to key power units that are prioritized for restoration, such as photovoltaic (PV) nodes, energy storage (ESS) nodes, and key load nodes like hospitals, used to construct the first-stage power supply backbone, which can significantly improve system restoration efficiency. The upper-level planning model can refer to a restoration sequence optimization model, used to generate restoration sequences that maximize the utilization of critical loads and renewable energy. The lower-level planning model can refer to a path search model, outputting the optimal switching operation sequence for topological connectivity. The first power supply topology can refer to a phased network structure, such as a radial network including PV, energy storage, and ICU loads generated using Dijkstra's algorithm, used to ensure rapid energization of core nodes.

[0064] Step 103: The second optimization stage includes: based on the comprehensive power parameters and the first power supply topology, combined with a preset optimization model, determining the recovery order and recovery path of the remaining nodes in the power system to be restored, and obtaining a second power supply topology including all nodes, wherein the remaining nodes are nodes other than the target micro source.

[0065] The second power supply topology can refer to a complete network recovery structure used to achieve 100% energized nodes across the entire network, ensuring overall system power supply reliability. Remaining nodes can refer to non-critical power units, such as non-target micro-source nodes including residential loads and general commercial loads. The preset optimization model can refer to a multi-objective decision model, such as using the Floyd algorithm combined with mixed integers.

[0066] Step 104: Perform power restoration on the power system to be restored according to the second power supply topology.

[0067] The beneficial effects of one of the embodiments in this specification include at least the following: By addressing the hierarchical and constraint complexity of the two-stage optimization model for microgrid black start, a Benders two-stage solution algorithm incorporating an adaptive penalty factor is proposed. The first optimization stage optimizes the micro-source recovery sequence and path based on the Benders decomposition method with an adaptive penalty factor; the second optimization stage combines mixed-integer programming to optimize load recovery. This invention improves the accuracy of the photovoltaic-storage model through dynamic characteristic correction, balances recovery efficiency and stability through a two-stage framework, and enhances solution performance through an adaptive algorithm, effectively achieving efficient and safe recovery from microgrid black start.

[0068] In some implementations, the upper-level planning model includes:

[0069] in, This represents the maximum value of the upper-level planning model during multiple iterations. This represents the amount of load restoration within the energized area of ​​Phase 1; This is the load recovery adjustment coefficient, used to characterize the degree of recovery of the out-of-power load; These are auxiliary variables for lower-level planning, used to integrate lower-level constraints; This represents the integral sum of available photovoltaic active power output during the black start recovery process of a microgrid. This represents the integral sum of the available active power output of the energy storage system during the black start recovery process of a microgrid. This is a penalty factor.

[0070] In some implementations, the step of calculating the integral sum of available photovoltaic active power output during the microgrid black-start recovery process includes: Based on comprehensive power parameters, the photovoltaic output at each time step is calculated; Based on the photovoltaic output at each time step, the integral sum of the available photovoltaic active power output is calculated. The constraint expressions for calculating the photovoltaic output at each time step include:

[0071] in, It is a collection of distributed photovoltaic systems within a microgrid; This refers to the operating status of distributed photovoltaic (PV) systems. For the active power output of distributed photovoltaic r in the t-th time step, Let r be the reactive power output of the distributed photovoltaic system in the t-th time step; Let r be the predicted active power value of the distributed photovoltaic system at time step t. Let r be the predicted reactive power output of the distributed photovoltaic system at the t-th time step.

[0072] In some implementations, the step of calculating the predicted active power of photovoltaic power includes: Based on comprehensive power parameters, the dynamic starting power correction coefficient is calculated, and the corresponding calculation formula includes:

[0073]

[0074] in, The reference correction factor (range 0.8~0.9) is used under standard test conditions (illuminance G0=1000W / m2, component temperature T0=25℃). The light intensity factor reflects the compensation requirement for starting power when there is insufficient light. =0.3~0.5 is the light sensitivity coefficient, and G(t) is the actual light intensity at time t; Temperature influence factor ( ), reflecting the correction of starting power caused by the decrease in component efficiency at high temperatures; kT is the temperature coefficient (range -0.002~0.004℃). Let t be the component temperature at time step t; If photovoltaic power is a black-start power source, the available active power output is: , in, This is the predicted maximum photovoltaic output at time step t.

[0075] If the photovoltaic system is a non-self-starting micro-source, the usable active power output is:

[0076] in, This is the baseline value for starting power under standard conditions; This is the corrected actual starting power; To initiate the start step, To complete the step.

[0077] In some implementations, the step of calculating the integral sum of the available active power output of energy storage during the microgrid black-start recovery process includes: Based on comprehensive power parameters, calculate the energy storage output at each time step; Based on the energy storage output at each time step, calculate the integral sum of the available active power output of the energy storage. The constraint expressions for calculating the energy storage output at each time step include:

[0078] in, A collection of energy storage devices within a microgrid; This refers to the operating state of the energy storage device s; The charging state of the energy storage device s This represents the discharge state of the energy storage device s; The charging power of energy storage device s in the t-th time step, Let be the discharge power of energy storage device s in the t-th time step; The minimum charging power of the energy storage device s, The maximum charging power of the energy storage device s; The minimum discharge power of the energy storage device s, denoted as s, representing the maximum discharge power of the energy storage device.

[0079] In some implementations, the step of calculating the active power prediction value of energy storage includes: Based on comprehensive power parameters, the dynamic discharge efficiency is calculated, and the corresponding formulas include:

[0080] in, The energy storage discharge efficiency varies with the remaining energy (state of charge (SOC(t))) and the number of charge-discharge cycles. Dynamic correction; The baseline discharge efficiency under standard conditions for the new equipment (values ​​range from 0.9 to 0.95); h(SOC(t)) is the residual energy influence factor; This represents the remaining energy at time step t. This represents the maximum energy storage capacity. The number of cycles is the influencing factor; Ncyc is the cumulative number of charge-discharge cycles, and each complete charge-discharge cycle is counted as one cycle; Based on the calculated dynamic discharge efficiency, the formula for calculating the corrected energy storage output includes:

[0081] in, This represents the maximum discharge power of the energy storage. Minimum capacity limit; The time step length.

[0082] In some implementations, the lower-level planning model includes:

[0083] in, This represents the maximum value of the lower-level planning model during multiple iterations. Let be the importance of the i-th node. Let be the line weight of the j-th line.

[0084] In some implementations, the formula for calculating node importance includes:

[0085] in, The normalized node degree (reflecting topological connectivity) is defined as the ratio of the number of connections a node has to the maximum node degree in the entire network. The normalized load contribution is the ratio of the load power carried by a node to the load power of the largest node in the entire network. The normalized load level contribution is obtained by standardizing the load level weights connected to the node (Level 1 load 1.0, Level 2 load 0.2, Level 3 load 0.01). For node degree, Contribution to node load Weighting coefficients for the contribution of load level.

[0086] In some implementations, the formula for calculating the line weights includes:

[0087] in, This is the normalized path betweenness (reflecting topological criticality), which is the percentage of frequency that path j appears in the shortest paths of the entire network; The normalized line charging capacitor (reflecting overvoltage risk) has a higher weighting value for the larger the capacitor. The normalized line recovery time (reflecting operational efficiency) has a higher weighting for longer recovery times. , and These are the weighting coefficients for line side betweenness, line charging capacitance, and line recovery time, respectively.

[0088] In some implementations, the optimization model for the second optimization stage includes:

[0089] In the formula, This marks the end of the first phase. The duration of the second phase; Let be the total active power of the load that has been restored at time t; Let be the active power of the restored load at node i. The set of loads that have been restored at time t; Importance-weighted power for restored loads. Let be the weight of the i-th node; and Weighting coefficients ( , usually take , These figures respectively reflect the emphasis on the amount of recovery and its importance.

[0090] As a specific example: like Figure 2 As shown, Phase 2 is based on the power supply topology obtained in Phase 1, further restoring the nodes, lines, and loads that are still in a power outage state, ultimately restoring the power supply to the entire microgrid. Phase 2 only needs to consider the line weights, therefore the Floyd algorithm is used to directly solve for the restoration paths of the remaining nodes.

[0091] like Figure 3 As shown, for the bilevel programming problem in the first stage of a two-stage programming model, the traditional Benders decomposition method is prone to slow convergence or insufficient accuracy when solving such strongly coupled problems. Therefore, an adaptive penalty factor is introduced to dynamically balance the constraint strengths of the upper and lower levels, as specifically implemented below: Benders decomposition method solves a bi-level programming problem iteratively through a "master problem-subproblem" approach. The master problem is the upper-level programming problem, aiming to maximize the available active power output of the microgrid. It determines the recovery time and sequence of non-self-starting micro-sources, transforming the lower-level path constraints into auxiliary variables and cut plane constraints. The objective function is:

[0092] In the formula, This represents the amount of load restoration within the energized area of ​​Phase 1; This is the load recovery adjustment coefficient, used to characterize the degree of recovery of the out-of-power load; These serve as auxiliary variables for lower-level planning, used to integrate path constraints from sub-problem feedback. , These represent the available active power output from photovoltaics and the available active power output from energy storage during the black start recovery process of a microgrid, respectively. The penalty factor is used. The subproblem is a lower-level programming problem. Based on the recovery order given in the upper level, the goal is to maximize the sum of node importance and route safety of the recovery path, and search for the optimal recovery path. The objective function is:

[0093] In the formula, For node importance, This represents the line weights.

[0094] In some implementations, the constraints on the penalty factor include: Define the deviation rate of the upper and lower objective functions ,

[0095] in, Mapping the optimal solution of the subproblem to the equivalent objective value of the upper level. The larger the value, the more significant the difference between the upper and lower level solutions; During the iteration process, when At that time, increase ( ), This represents the penalty factor for the current iteration. This represents the penalty factor for the previous iteration, which strengthens the constraint of the subproblem on the main problem and speeds up convergence to the feasible region. when And relative gap , reduce ( Weakening constraints releases the optimization space of the main problem and improves solution accuracy; when At that time, keep The convergence speed and accuracy remain unchanged; To avoid If the value is too large, it will cause instability; if it is too small, it will lose its constraint effect. Therefore, upper and lower limits should be set. .

[0096] In some implementations, the iterative solution process of the Benders decomposition method incorporating an adaptive penalty factor includes: Step 1: Initialization, setting the initial penalty factor The iteration counter k=0, the maximum number of iterations kmax=50, and the convergence threshold gap*=0.05; Step 2: Solve the main problem, based on the current... By cutting the historical plane, the micro-source recovery order and the upper-level target value are obtained. Update the Nether ; Step 3: Solve the subproblems, and based on the recovery order of the upper level, obtain the optimal path and the objective value of the subproblems. Mapped to the upper layer Update Upper Realm ; Step 4: Calculation and relative gap Adjust according to the rules ; Step 5: Generate cutting planes. Based on the dual solutions of the subproblems, generate optimal or feasible cuts and add them to the constraints of the main problem. Step 6: If or If the iteration terminates, output the micro-source recovery scheme; otherwise, k=k+1 and return to step 2.

[0097] Figure 4 The microgrid topology provided for embodiments of the invention. A transformer substation topology is established using IEEE 24 nodes.

[0098] The beneficial effects of this invention are as follows: First, for photovoltaic and energy storage devices in the black start process of microgrids, a power output model considering dynamic characteristic correction is constructed. By introducing the influence factors of light intensity, temperature, remaining energy, and cycle number, the power output calculation parameters of photovoltaic and energy storage are dynamically adjusted, which effectively improves the adaptability of the model to complex environment and equipment status changes, and significantly improves the accuracy of power prediction and scheduling in the black start process.

[0099] Second, combining the dynamic recovery characteristics of microgrid black start, a two-stage collaborative optimization framework of "micro-source priority recovery - load hierarchical recovery" is proposed. The upper and lower stages are linked through power supply topology transmission and power constraint feedback. It does not rely on external large power supply support. It can complete the whole process from micro-source start-up to load recovery by using only the microgrid's own photovoltaic and energy storage resources. This provides a systematic recovery path planning method for black start of microgrids with a high proportion of new energy.

[0100] Third, the control method takes the safety and stability of the microgrid black start process as a premise, and comprehensively considers system constraints such as power balance and power flow constraints. By solving the two-stage optimization model through the Benders decomposition method with adaptive penalty factor and Floyd algorithm, the total black start time is shortened while ensuring the priority recovery of critical loads and the stability of system frequency and voltage. This reduces the losses of photovoltaic and energy storage equipment caused by frequent start-stop or power fluctuations, and improves the efficiency and economy of microgrid black start.

[0101] Corresponding to the above method embodiments, this specification also provides an embodiment of a microgrid black-start recovery optimization device based on adaptive Benders decomposition. Figure 5 This specification illustrates a schematic diagram of a microgrid black-start recovery optimization device based on adaptive Benders decomposition, provided in some embodiments. Figure 5 As shown, the device includes: The acquisition module is used to acquire the comprehensive power parameters of the power system to be restored, and determine the power supply of all nodes in the power system to be restored according to two preset optimization stages; The first optimization module includes: determining the restoration order of multiple target micro-source nodes in the power system to be restored based on comprehensive power parameters and a two-level programming model constructed using the Benders decomposition method with adaptive adjustment of penalty factors; determining the restoration path based on the restoration order; and generating a first power supply topology including the target micro-source nodes. The two-level programming model includes an upper-level programming model for determining the restoration order and a lower-level programming model for determining the restoration path. The target micro-source nodes include photovoltaic nodes, energy storage nodes, and key load nodes. The second optimization module is used to: determine the restoration order and restoration path of the remaining nodes in the power system to be restored based on the comprehensive power parameters and the first power supply topology, combined with a preset optimization model, to obtain a second power supply topology that includes all nodes, wherein the remaining nodes are nodes other than the target micro source; The recovery module is used to restore power to the power system to be restored according to the second power supply topology.

[0102] In some implementations, the upper-level planning model includes:

[0103] in, This represents the maximum value of the upper-level planning model during multiple iterations. This represents the amount of load restoration within the energized area of ​​Phase 1; This is the load recovery adjustment coefficient, used to characterize the degree of recovery of the out-of-power load; These are auxiliary variables for lower-level planning, used to integrate lower-level constraints; This represents the integral sum of available photovoltaic active power output during the black start recovery process of a microgrid. This represents the integral sum of the available active power output of the energy storage system during the black start recovery process of a microgrid. This is a penalty factor.

[0104] In some implementations, the step of calculating the integral sum of available photovoltaic active power output during the microgrid black-start recovery process includes: Based on comprehensive power parameters, the photovoltaic output at each time step is calculated; Based on the photovoltaic output at each time step, the integral sum of the available photovoltaic active power output is calculated. The constraint expressions for calculating the photovoltaic output at each time step include:

[0105] in, It is a collection of distributed photovoltaic systems within a microgrid; This refers to the operating status of distributed photovoltaic (PV) systems. For the active power output of distributed photovoltaic r in the t-th time step, Let r be the reactive power output of the distributed photovoltaic system in the t-th time step; Let r be the predicted active power value of the distributed photovoltaic system at time step t. Let r be the predicted reactive power output of the distributed photovoltaic system at the t-th time step.

[0106] In some implementations, the step of calculating the predicted active power of photovoltaic power includes: Based on comprehensive power parameters, the dynamic starting power correction coefficient is calculated, and the corresponding calculation formula includes:

[0107]

[0108] in, The reference correction factor (range 0.8~0.9) is used under standard test conditions (illuminance G0=1000W / m2, component temperature T0=25℃). The light intensity factor reflects the compensation requirement for starting power when there is insufficient light. =0.3~0.5 is the light sensitivity coefficient, and G(t) is the actual light intensity at time t; Temperature influence factor ( ), reflecting the correction of starting power caused by the decrease in component efficiency at high temperatures; kT is the temperature coefficient (range -0.002~0.004℃). Let t be the component temperature at time step t; If photovoltaic power is a black-start power source, the available active power output is: , in, This is the predicted maximum photovoltaic output at time step t.

[0109] If the photovoltaic system is a non-self-starting micro-source, the usable active power output is:

[0110] in, This is the baseline value for starting power under standard conditions; This is the corrected actual starting power; To initiate the start step, To complete the step.

[0111] In some implementations, the step of calculating the integral sum of the available active power output of energy storage during the microgrid black-start recovery process includes: Based on comprehensive power parameters, calculate the energy storage output at each time step; Based on the energy storage output at each time step, calculate the integral sum of the available active power output of the energy storage. The constraint expressions for calculating the energy storage output at each time step include:

[0112] in, A collection of energy storage devices within a microgrid; This refers to the operating state of the energy storage device s; The charging state of the energy storage device s This represents the discharge state of the energy storage device s; The charging power of energy storage device s in the t-th time step, Let be the discharge power of energy storage device s in the t-th time step; The minimum charging power of the energy storage device s, The maximum charging power of the energy storage device s; The minimum discharge power of the energy storage device s, denoted as s, representing the maximum discharge power of the energy storage device.

[0113] In some implementations, the step of calculating the active power prediction value of energy storage includes: Based on comprehensive power parameters, the dynamic discharge efficiency is calculated, and the corresponding formulas include:

[0114] in, The energy storage discharge efficiency varies with the remaining energy (state of charge (SOC(t))) and the number of charge-discharge cycles. Dynamic correction; The baseline discharge efficiency under standard conditions for the new equipment (values ​​range from 0.9 to 0.95); h(SOC(t)) is the residual energy influence factor; This represents the remaining energy at time step t. This represents the maximum energy storage capacity. The number of cycles is the influencing factor; Ncyc is the cumulative number of charge-discharge cycles, and each complete charge-discharge cycle is counted as one cycle; Based on the calculated dynamic discharge efficiency, the formula for calculating the corrected energy storage output includes:

[0115] in, This represents the maximum discharge power of the energy storage. Minimum capacity limit; The time step length.

[0116] In some implementations, the lower-level planning model includes:

[0117] in, This represents the maximum value of the lower-level planning model during multiple iterations. Let be the importance of the i-th node. Let be the line weight of the j-th line.

[0118] In some implementations, the formula for calculating node importance includes:

[0119] in, The normalized node degree (reflecting topological connectivity) is defined as the ratio of the number of connections a node has to the maximum node degree in the entire network. The normalized load contribution is the ratio of the load power carried by a node to the load power of the largest node in the entire network. The normalized load level contribution is obtained by standardizing the load level weights connected to the node (Level 1 load 1.0, Level 2 load 0.2, Level 3 load 0.01). For node degree, Contribution to node load Weighting coefficients for the contribution of load level.

[0120] In some implementations, the formula for calculating the line weights includes:

[0121] in, This is the normalized path betweenness (reflecting topological criticality), which is the percentage of frequency that path j appears in the shortest paths of the entire network; The normalized line charging capacitor (reflecting overvoltage risk) has a higher weighting value for the larger the capacitor. The normalized line recovery time (reflecting operational efficiency) has a higher weighting for longer recovery times. , and These are the weighting coefficients for line side betweenness, line charging capacitance, and line recovery time, respectively.

[0122] In some implementations, the optimization model for the second optimization stage includes:

[0123] In the formula, This marks the end of the first phase. The duration of the second phase; Let be the total active power of the load that has been restored at time t; Let be the active power of the restored load at node i. The set of loads that have been restored at time t; Importance-weighted power for restored loads. Let be the weight of the i-th node; and Weighting coefficients ( , usually take , These figures respectively reflect the emphasis on the amount of recovery and its importance.

[0124] The above is a schematic scheme of a microgrid black-start recovery optimization device based on adaptive Benders decomposition according to this embodiment. It should be noted that the technical solution of this microgrid black-start recovery optimization device based on adaptive Benders decomposition belongs to the same concept as the technical solution of the microgrid black-start recovery optimization method based on adaptive Benders decomposition described above. Details not described in detail in the technical solution of the microgrid black-start recovery optimization device based on adaptive Benders decomposition can be found in the description of the technical solution of the microgrid black-start recovery optimization method based on adaptive Benders decomposition described above.

[0125] Figure 6 A structural block diagram of a computing device 600 according to some embodiments of this specification is shown. The components of the computing device 600 include, but are not limited to, a memory 601 and a processor 602. The processor 602 is connected to the memory 601 via a bus 603, and a database 605 is used to store data.

[0126] The computing device 600 also includes an access device 604 that enables the computing device 600 to communicate via one or more networks 606. Examples of these networks include Public Switched Telephone Network (PSTN), Local Area Network (LAN), Wide Area Network (WAN), Personal Area Network (PAN), or combinations of communication networks such as the Internet. The access device 604 may include one or more of any type of wired or wireless network interface (e.g., a network interface card (NIC)), such as an IEEE 802.11 Wireless Local Area Network (WLAN) wireless interface, a Wi-MAX (Worldwide Interoperability for Microwave Access) interface, an Ethernet interface, a Universal Serial Bus (USB) interface, a cellular network interface, a Bluetooth interface, or a Near Field Communication (NFC) interface.

[0127] In one embodiment of this specification, the above-described components of the computing device 600 and Figure 6 Other components, not shown, can also be connected to each other, for example, via a bus. It should be understood that... Figure 6 The block diagram of the computing device shown is for illustrative purposes only and is not intended to limit the scope of this specification. Those skilled in the art can add or replace other components as needed.

[0128] The computing device 600 can be any type of stationary or mobile computing device, including mobile computers or mobile computing devices (e.g., tablet computers, personal digital assistants, laptop computers, notebook computers, netbooks, etc.), mobile phones (e.g., smartphones), wearable computing devices (e.g., smartwatches, smart glasses, etc.) or other types of mobile devices, or stationary computing devices such as desktop computers or personal computers (PCs). The computing device 600 can also be a mobile or stationary server.

[0129] The processor 602 executes the following computer-executable instructions, which, when executed by the processor, implement the steps of the microgrid black-start recovery optimization method based on adaptive Benders decomposition described above. The above is an illustrative scheme of a computing device according to this embodiment. It should be noted that the technical solution of this computing device and the technical solution of the microgrid black-start recovery optimization method based on adaptive Benders decomposition described above belong to the same concept. Details not described in detail in the technical solution of the computing device can be found in the description of the technical solution of the microgrid black-start recovery optimization method based on adaptive Benders decomposition described above.

[0130] An embodiment of this specification also provides a computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the microgrid black-start recovery optimization method based on adaptive Benders decomposition described above.

[0131] The above is an illustrative scheme of a computer-readable storage medium according to this embodiment. It should be noted that the technical solution of this storage medium belongs to the same concept as the technical solution of the microgrid black-start recovery optimization method based on adaptive Benders decomposition described above. Details not described in detail in the technical solution of the storage medium can be found in the description of the technical solution of the microgrid black-start recovery optimization method based on adaptive Benders decomposition described above.

[0132] An embodiment of this specification also provides a computer program, wherein when the computer program is executed in a computer, the computer is instructed to perform the steps of the microgrid black-start recovery optimization method based on adaptive Benders decomposition described above.

[0133] The above is an illustrative scheme of a computer program according to this embodiment. It should be noted that the technical solution of this computer program belongs to the same concept as the technical solution of the microgrid black-start recovery optimization method based on adaptive Benders decomposition described above. For details not described in detail in the technical solution of the computer program, please refer to the description of the technical solution of the microgrid black-start recovery optimization method based on adaptive Benders decomposition described above.

[0134] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0135] The computer instructions include computer program code, which may be in the form of source code, object code, executable file, or certain intermediate forms. The computer-readable medium may include any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium may be appropriately added to or subtracted according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media may not include electrical carrier signals and telecommunication signals.

[0136] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0137] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0138] The preferred embodiments disclosed above are merely illustrative of this specification. The optional embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this invention. These embodiments are selected and specifically described in this specification to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize this specification. This specification is limited only by the claims and their full scope and equivalents.

Claims

1. A microgrid black-start recovery optimization method based on adaptive Benders decomposition, characterized in that, include: Obtain comprehensive power parameters of the power system to be restored, and determine the power supply of all nodes in the power system to be restored according to two preset optimization stages; The first optimization stage includes: determining the recovery order of multiple target micro-source nodes in the power system to be restored based on the comprehensive power parameters and a two-level programming model constructed using the Benders decomposition method with adaptive adjustment of penalty factors; determining the recovery path based on the recovery order; and generating a first power supply topology including the target micro-source nodes. The two-level programming model includes an upper-level programming model for determining the recovery order and a lower-level programming model for determining the recovery path. The target micro-source nodes include photovoltaic nodes, energy storage nodes, and key load nodes. The second optimization stage includes: based on the comprehensive power parameters and the first power supply topology, combined with a preset optimization model, determining the recovery order and recovery path of the remaining nodes in the power system to be restored, and obtaining a second power supply topology including all nodes, wherein the remaining nodes are nodes other than the target micro source; Power is restored to the power system to be restored according to the second power supply topology.

2. The method according to claim 1, characterized in that, The upper-level planning model includes: in, This represents the maximum value of the upper-level planning model during multiple iterations. This represents the amount of load restoration within the energized area of ​​Phase 1; This is the load recovery adjustment coefficient, used to characterize the degree of recovery of the out-of-power load; These are auxiliary variables for lower-level planning, used to integrate lower-level constraints; This represents the integral sum of available photovoltaic active power output during the black start recovery process of a microgrid. This represents the integral sum of the available active power output of the energy storage system during the black start recovery process of a microgrid. This is a penalty factor.

3. The method according to claim 2, characterized in that, The steps for calculating the integral sum of available photovoltaic active power output during the black start recovery process of a microgrid include: Based on the comprehensive power parameters, the photovoltaic output at each time step is calculated; Based on the photovoltaic output at each time step, the integral sum of the available photovoltaic active power is calculated, wherein the constraint expressions for calculating the photovoltaic output at each time step include: in, It is a collection of distributed photovoltaic systems within a microgrid; This refers to the working state of distributed photovoltaic (PV) systems. For the active power output of distributed photovoltaic r in the t-th time step, Let r be the reactive power output of the distributed photovoltaic system in the t-th time step; Let r be the predicted active power value of the distributed photovoltaic system at time step t. Let r be the predicted reactive power output of the distributed photovoltaic system at the t-th time step.

4. The method according to claim 3, characterized in that, The steps for calculating the predicted active power of photovoltaic power include: Based on the comprehensive power parameters, the dynamic starting power correction coefficient is calculated, and the corresponding calculation formula includes: in, The reference correction factor (range 0.8~0.9) is used under standard test conditions (illuminance G0=1000W / m2, component temperature T0=25℃). This is the light intensity factor, which reflects the compensation requirement for starting power when there is insufficient light. =0.3~0.5 is the light sensitivity coefficient, and G(t) is the actual light intensity at time t; Temperature influence factor ( ), reflecting the correction of starting power caused by the decrease in component efficiency at high temperatures; kT is the temperature coefficient (range -0.002~0.004℃). Let t be the component temperature at time step t; If photovoltaic power is a black-start power source, the available active power output is: , in, This represents the predicted maximum photovoltaic output at time step t. If the photovoltaic system is a non-self-starting micro-source, the usable active power output is: in, This is the baseline value for starting power under standard conditions; This is the corrected actual starting power; To initiate the start step, To complete the step.

5. The method according to claim 2, characterized in that, The steps for calculating the integral sum of available active power output from energy storage during the black start recovery process of a microgrid include: Based on the comprehensive power parameters, the energy storage output at each time step is calculated; Based on the energy storage output at each time step, the integral sum of the available active power output of the energy storage is calculated, wherein the constraint expressions for calculating the energy storage output at each time step include: in, A collection of energy storage devices within a microgrid; This refers to the operating state of the energy storage device s; The charging state of the energy storage device s This represents the discharge state of the energy storage device s; The charging power of energy storage device s in the t-th time step, Let be the discharge power of energy storage device s in the t-th time step; The minimum charging power of the energy storage device s, The maximum charging power of the energy storage device s; The minimum discharge power of the energy storage device s, denoted as s, representing the maximum discharge power of the energy storage device.

6. The method according to claim 3, characterized in that, The steps for calculating the active power prediction value of energy storage include: Based on the aforementioned comprehensive power parameters, the dynamic discharge efficiency is calculated, and the corresponding calculation formula includes: in, The energy storage discharge efficiency varies with the remaining energy (state of charge (SOC(t))) and the number of charge-discharge cycles. Dynamic correction; The baseline discharge efficiency under standard conditions for the new equipment (values ​​range from 0.9 to 0.95); h(SOC(t)) is the residual energy influence factor; This represents the remaining energy at time step t. This represents the maximum energy storage capacity. The number of cycles is the influencing factor; Ncyc is the cumulative number of charge-discharge cycles, and each complete charge-discharge cycle is counted as one cycle; Based on the calculated dynamic discharge efficiency, the formula for calculating the corrected energy storage output includes: in, This represents the maximum discharge power of the energy storage. Minimum capacity limit; The time step length.

7. The method according to claim 2, characterized in that, The lower-level planning model includes: in, This represents the maximum value of the lower-level planning model during multiple iterations. Let be the importance of the i-th node. Let be the line weight of the j-th line.

8. The method according to claim 7, characterized in that, The formula for calculating the importance of the nodes includes: in, The normalized node degree (reflecting topological connectivity) is defined as the ratio of the number of connections a node has to the maximum node degree in the entire network. The normalized load contribution is the ratio of the load power carried by a node to the load power of the largest node in the entire network. The normalized load level contribution is obtained by standardizing the load level weights connected to the node (Level 1 load 1.0, Level 2 load 0.2, Level 3 load 0.01). For node degree, Contribution to node load Weighting coefficients for the contribution of load level.

9. The method according to claim 7, characterized in that, The formula for calculating the line weights includes: in, This is the normalized path betweenness (reflecting topological criticality), which is the percentage of frequency that path j appears in the shortest paths of the entire network; The normalized line charging capacitor (reflecting overvoltage risk) has a higher weighting value for the larger the capacitor. The normalized line recovery time (reflecting operational efficiency) has a higher weighting for longer recovery times. , and These are the weighting coefficients for line side betweenness, line charging capacitance, and line recovery time, respectively.

10. The method according to claim 1, characterized in that, The optimization model in the second optimization stage includes: In the formula, This marks the end of the first phase. The duration of the second phase; Let be the total active power of the load that has been restored at time t; Let be the active power of the restored load at node i. The set of loads that have been restored at time t; Importance-weighted power for restored loads. Let be the weight of the i-th node; and Weighting coefficients ( , usually take , These figures respectively reflect the emphasis on the amount of recovery and its importance.

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