A power transmission and distribution network collaborative load recovery method

Abstract

The application discloses a power transmission and distribution network collaborative load recovery method, and relates to the field of power transmission and distribution network load recovery.The method comprises the following steps: acquiring power transmission network side operation parameters and power distribution network side operation parameters; according to the power transmission network side operation parameters, taking the minimum total power transmission network weighted load reduction amount and recovery scheduling cost as the target, a power transmission network load recovery model is built; according to the power distribution network side operation parameters, taking the minimum total power distribution network weighted load reduction amount, recovery scheduling cost and line active power loss as the target, a power distribution network load recovery model is built; the load recovery model is augmented to obtain an augmented model; the alternating direction multiplier method is used for distributed iteration solving, and the optimal power transmission network and power distribution network operation parameters are determined to control the power transmission network and power distribution network operation, so that the collaborative load recovery of the power transmission and distribution network system is realized; and the application can guarantee frequency safety, efficiently support load recovery and reduce recovery scheduling cost.

Description

Technical Field

[0001] This application relates to the field of power transmission and distribution network load restoration, and in particular to a method for coordinated load restoration of power transmission and distribution networks. Background Technology

[0002] Against the backdrop of global climate change, increasingly frequent extreme natural disasters continue to threaten the safe and reliable power supply of power transmission and distribution networks, posing a serious threat to energy security and social development. At the same time, with the transformation of the power system's energy structure towards low carbon and the large-scale integration of new energy sources into the power transmission and distribution network, the system structure and operating characteristics are becoming increasingly complex, exhibiting characteristics of low inertia and weak support, and the risk of major power outages is significantly increasing.

[0003] In response to the frequency instability caused by the rapid grid connection of loads and the random fluctuations of new energy sources during the post-disaster recovery process, existing technologies lack research on post-disaster load recovery methods that meet the security and defense needs of new power systems, thus failing to improve the grid's ability to withstand extreme natural disasters while reducing power outage losses. Summary of the Invention

[0004] The purpose of this application is to provide a method for coordinated load restoration in power transmission and distribution networks, which can efficiently support load restoration and reduce restoration scheduling costs while ensuring frequency security.

[0005] To achieve the above objectives, this application provides the following solution.

[0006] This application provides a method for coordinated load restoration in a power transmission and distribution network, comprising: acquiring operating parameters of the transmission network side and operating parameters of the distribution network side; the operating parameters of the transmission network side include the load restoration amount of the transmission network, the power source operating status, and the multi-source frequency regulation reserve power in the power transmission and distribution network system; the operating parameters of the distribution network side include the load restoration amount of the distribution network, network loss variables, power source active power output, and multi-source frequency regulation reserve power in the power transmission and distribution network system; based on the operating parameters of the transmission network side, establishing a power transmission network load restoration model with the goal of minimizing the total weighted load reduction of the transmission network and minimizing the restoration scheduling cost; and based on the operating parameters of the distribution network side, minimizing the total weighted load reduction of the distribution network, minimizing the restoration scheduling cost, and minimizing the line... With the goal of minimizing active power loss, a distribution network load recovery model is constructed. The transmission network load recovery model and the distribution network load recovery model are augmented to obtain augmented transmission network models and augmented distribution network models, respectively. Based on these models, a distributed iterative solution using the alternating direction multiplier method is employed to determine the optimal transmission network-side operating parameters and the optimal distribution network-side operating parameters. The operation of the transmission network is controlled according to the optimal transmission network-side operating parameters, and the operation of the distribution network is controlled according to the optimal distribution network-side operating parameters to achieve coordinated load recovery of the transmission and distribution network system.

[0007] Based on the specific embodiments provided in this application, the following technical effects are disclosed.

[0008] This application provides a method for coordinated load restoration in transmission and distribution networks. By acquiring operating parameters from both the transmission and distribution networks, it accurately covers key dispatching elements such as load restoration, generator operation, frequency regulation reserves, and network losses, making subsequent modeling and optimization solutions more closely aligned with actual engineering operation scenarios in transmission and distribution networks. A transmission network load restoration model is built with the goal of minimizing the total weighted load reduction and restoration dispatching costs. This model, while prioritizing grid power supply reliability, balances the degree of load restoration with dispatching cost requirements, effectively balancing the power supply priority of important loads with the cost of restoration dispatching, making the transmission network load restoration scheme both practical and economical. Similarly, a distribution network load restoration model is built with the goal of minimizing the total weighted load reduction, restoration dispatching costs, and line active power losses. This model balances power supply restoration, dispatching costs, and grid energy efficiency, reducing load losses and dispatching costs after faults while also mitigating [the impact of faults]. This method addresses active power loss in distribution network lines and improves resource utilization efficiency. By constructing augmented models for both transmission and distribution networks, augmented terms are introduced into the original load recovery model to resolve variable coupling conflicts caused by the segmented modeling of transmission and distribution networks. This transforms the non-distributed optimization model into a standard form suitable for distributed iterative solutions. The method of alternating direction multipliers is used for distributed iterative solutions to determine the optimal operating parameters for both transmission and distribution networks. This enables hierarchical decoupling and parallel optimization of transmission and distribution networks, achieving global collaborative optimization without centralized scheduling. This improves the stability of the solution results and ensures that the obtained operating parameters meet the constraints and multi-objective optimization requirements of each level of the power grid. By controlling the operation of the transmission and distribution system based on the optimal operating parameters, the optimal optimization decisions obtained from the model solution are directly implemented into actual power grid control commands, enabling safe, economical, and efficient collaborative load recovery after transmission and distribution network system failures. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is an application environment diagram of a power transmission and distribution network coordinated load restoration method according to an embodiment of this application.

[0011] Figure 2 This is a flowchart illustrating a method for coordinated load restoration of a power transmission and distribution network, provided as an embodiment of this application.

[0012] Figure 3 This is a schematic diagram of the overall framework of a method for coordinated load restoration of power transmission and distribution networks, provided as an embodiment of this application.

[0013] Figure 4 This is a schematic diagram showing the variation of the lowest system frequency under different test scenarios in an embodiment of this application.

[0014] Figure 5 This is a schematic diagram of the parameter sensitivity analysis results provided in an embodiment of this application. Detailed Implementation

[0015] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0016] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0017] The transmission and distribution network coordinated load restoration method provided in this application embodiment can be applied to, for example, Figure 1In the application environment shown, terminal 101 communicates with server 102 via a network. A data storage system can store the data that server 102 needs to process. The data storage system can be set up independently, integrated into server 102, or placed in the cloud or on another server. Terminal 101 can send transmission network-side operating parameters and distribution network-side operating parameters to server 102. Server 102 receives these parameters, builds load recovery and augmented models based on them, and uses the alternating direction multiplier method for distributed iterative solving to determine the optimal transmission network-side and optimal distribution network-side operating parameters. These parameters are then used to control the operation of the transmission and distribution networks respectively, achieving coordinated load recovery of the transmission and distribution network systems. Server 102 can then feed back the obtained optimal transmission network-side and optimal distribution network-side operating parameters to terminal 101. Furthermore, in some embodiments, the transmission and distribution network coordinated load restoration method can also be implemented separately by the server 102 or the terminal 101. For example, the terminal 101 can directly build a load restoration model and an augmented model based on the transmission network side operating parameters and the distribution network side operating parameters, and use the alternating direction multiplier method for distributed iterative solution to determine the optimal transmission network side operating parameters and the optimal distribution network side operating parameters, so as to control the operation of the transmission network and the distribution network respectively and realize the coordinated load restoration of the transmission and distribution network system. Alternatively, the server 102 can obtain the transmission network side operating parameters and the distribution network side operating parameters from the data storage system to build a load restoration model and an augmented model, and use the alternating direction multiplier method for distributed iterative solution to determine the optimal transmission network side operating parameters and the optimal distribution network side operating parameters, so as to control the operation of the transmission network and the distribution network respectively and realize the coordinated load restoration of the transmission and distribution network system.

[0018] The terminal 101 can be, but is not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle devices. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. The server 102 can be implemented using a standalone server or a server cluster composed of multiple servers, or it can be a cloud server.

[0019] In one exemplary embodiment, such as Figure 2 As shown, a method for coordinated load restoration in a power transmission and distribution network is provided. This method is executed by computer equipment, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 Taking server 102 as an example, the explanation includes the following steps 201 to 206.

[0020] Step 201: Obtain the operating parameters of the transmission network and the distribution network. The transmission network operating parameters include the load recovery amount, power source operating status, and multi-source frequency regulation reserve power of the transmission network in the transmission and distribution network system. The distribution network operating parameters include the load recovery amount, network loss variables, active power output, and multi-source frequency regulation reserve power of the distribution network in the transmission and distribution network system.

[0021] Step 202: Based on the transmission network side operating parameters, and with the goal of minimizing the total weighted load reduction of the transmission network and minimizing the restoration scheduling cost, a transmission network load restoration model is built.

[0022] Step 203: Based on the operating parameters of the distribution network side, a distribution network load recovery model is built with the objectives of minimizing the total weighted load reduction of the distribution network, minimizing the restoration and dispatching costs, and minimizing the active power loss of the lines.

[0023] Step 204: Augment the transmission network load recovery model and the distribution network load recovery model respectively to obtain the transmission network augmented model and the distribution network augmented model.

[0024] Step 205: Based on the transmission network load recovery model, the distribution network load recovery model, the transmission network augmentation model, and the distribution network augmentation model, the alternating direction multiplier method is used for distributed iterative solution to determine the optimal transmission network side operating parameters and the optimal distribution network side operating parameters.

[0025] Step 206: Control the operation of the transmission network according to the optimal transmission network side operating parameters, and control the operation of the distribution network according to the optimal distribution network side operating parameters, so as to realize the coordinated load recovery of the transmission and distribution network system.

[0026] In one example, such as Figure 3 As shown, the method for coordinated load restoration of power transmission and distribution networks includes the following steps A to C.

[0027] Step A: Construct a dynamic frequency response model and derive the dynamic frequency security constraints of the transmission and distribution network.

[0028] Specifically, regarding the frequency security issue during the load restoration process of the power transmission and distribution network system, the dynamic frequency response process of the power transmission and distribution network system is analyzed, a corresponding dynamic frequency response model is constructed, and then the dynamic frequency security constraints of the power transmission and distribution network are established.

[0029] Step B: Build a load recovery model for the power transmission and distribution network with embedded dynamic frequency security constraints within the system architecture.

[0030] Specifically, a transmission network load recovery model is built with the goal of minimizing the total weighted load reduction of the transmission network and the cost of restoration and dispatch. A distribution network load recovery model is built with the goal of minimizing the total weighted load reduction of the distribution network, line active power loss, and the cost of restoration and dispatch. A transmission and distribution network coordinated load recovery optimization model with embedded dynamic frequency security constraints is established under the system architecture.

[0031] Step C proposes an adaptive regularized alternating direction multiplier method based on inner and outer double-layer loops, which decomposes the original model into alternating solutions for the transmission network and distribution network models.

[0032] Specifically, this application proposes an adaptive regularized alternating direction multiplier method based on inner and outer double-layer cycles, which decomposes the original model into transmission network and distribution network sub-models for alternating solution.

[0033] In one example, the dynamic frequency security constraints of the power transmission and distribution network include the frequency change rate constraint, the frequency minimum point constraint, and the primary frequency regulation reserve power capacity constraint of the power transmission and distribution network system.

[0034] The method for establishing dynamic frequency security constraints for the power transmission and distribution network includes the following steps 301 to 304.

[0035] Step 301: Obtain the load grid connection imbalance power and the output fluctuation imbalance power of the power transmission and distribution network system, and determine the power imbalance power of the power transmission and distribution network based on the load grid connection imbalance power and the output fluctuation imbalance power.

[0036] Step 302: Construct the primary frequency regulation response characteristic model and the first-order time-domain swing equation of the power transmission and distribution network system.

[0037] Step 303: Perform inertia modeling on the transmission network and the distribution network respectively to obtain the total inertia of the transmission network and the total inertia of the distribution network, and calculate the equivalent total inertia of the transmission and distribution networks based on the total inertia of the transmission network and the total inertia of the distribution network.

[0038] Step 304: Based on the equivalent total inertia of the transmission and distribution network, the primary frequency regulation response characteristic model, the first-order time-domain swing equation, and the unbalanced power of the transmission and distribution network, construct the frequency change rate constraint, the frequency minimum point constraint, and the primary frequency regulation reserve power capacity constraint.

[0039] In one example, step A above can be replaced by steps A1 to A3.

[0040] Step A1, inertial response capability modeling.

[0041] On the transmission grid side, thermal power units rely on the inertia of synchronous machines to form physical inertia support, while wind power and electrochemical energy storage can rely on virtual synchronous machine technology to simulate the dynamic characteristics of synchronous machines, providing virtual inertia and jointly participating in the system's inertial response, thereby improving the grid's ability to withstand disturbances. The total inertia of the transmission grid is shown in the following formula.

[0042] .

[0043] in, for t Total inertia of the power grid during a given period For power transmission network nodes i The inertial time constant of the thermal power unit at that location, For power transmission network nodes i The rated capacity of the thermal power units at the location, for t Time-of-use transmission network nodes i The operating status variable for the thermal power unit at this location has a value of 1 indicating that it is in operation and a value of 0 indicating that it is out of operation. The set of nodes connected to thermal power units in the power transmission network. For power transmission network nodes i The inertial time constant of the wind turbine at that location. For power transmission network nodes i The rated capacity of the wind turbine units at the location, for t Time-of-use transmission network nodes i The wind turbine's operating status variable is set to 1, indicating it is in operation, and 0, indicating it is out of operation. The set of nodes connected to wind turbines in the power transmission network. For power transmission network nodes i Electrochemical energy storage inertial time constant at the location, For transmission network nodes i The rated power of the electrochemical energy storage at the location, It is the set of nodes in the power transmission network that are connected to electrochemical energy storage.

[0044] On the distribution network side, diesel engine generators (DEGs), as rotating power sources, can provide natural inertia support. Distributed photovoltaic (DPV) units and distributed energy systems (DES) can also provide corresponding power support by simulating the rotor inertia of a synchronous machine through virtual synchronous machine control. The total inertia of the distribution network is shown in the following formula.

[0045] .

[0046] in, for t Total inertia of the distribution network during a given time period For the first m Distribution network nodes i The inertial time constant of the diesel generator connected to the location. For the first m Distribution network nodes i The rated power of the diesel generator connected to the premises. For the first m The set of all nodes in a power distribution network that are connected to diesel generators. For the first m Distribution network nodes i The inertial time constant of the distributed photovoltaic (PV) units connected to the location. For the first m Distribution network nodes i The rated capacity of the distributed photovoltaic units connected to the premises, for t Time period m Distribution network nodes i The status variable for the distributed photovoltaic (PV) units connected to the site has a value of 1 indicating that it is in operation and a value of 0 indicating that it is out of operation. For the first m The set of all nodes in a power distribution network that are connected to distributed photovoltaic units. For the first m Distribution network nodes i The inertial time constant of the distributed energy system connected to the location. For the first m Distribution network nodes i The rated power of the distributed energy system connected to the premises For the first m The set of all nodes in a distribution network that are connected to a distributed energy system.

[0047] The equivalent total inertia of a power transmission and distribution network is composed of the total inertia of the power transmission network and the total inertia of the distribution network. Its calculation formula is as follows.

[0048] .

[0049] in, for t The equivalent total inertia of the power transmission and distribution network during a given time period. It is the set of all distribution networks in the power transmission and distribution network system.

[0050] Step A2, PFR characteristic modeling.

[0051] Under rapidly changing frequency regulation demands during load recovery, relying solely on synchronous generators is insufficient to stabilize the system frequency. In contrast, while wind and solar renewable energy and energy storage have limited frequency regulation capacity, their rapid response capabilities can effectively suppress frequency fluctuations and shorten recovery time. Taking into account the differences in response delays among various types of frequency regulation resources, a PFR characteristic model for the transmission and distribution network system is constructed as shown in the following equation.

[0052] .

[0053] in, for t Time-of-use transmission and distribution network PFR power, For PFR response delay of electrochemical energy storage, For PFR response delay of wind and solar new energy. For the PFR response delay of the diesel generator, For the PFR response delay of thermal power units The PFR ramp-up time constant for electrochemical energy storage The ramp-up time constant for wind and solar new energy PFR. The PFR (Progression Rate) ramp time constant of the diesel generator. This represents the PFR ramp-up time constant for thermal power units. for t The sum of the PFR (Power Reserve Ratio) of the power transmission and distribution network system during the time period. for t The sum of the standby power of wind and solar renewable energy in the power transmission and distribution network system during the time period. for t PFR standby power of diesel generator during the period for t PFR standby power of thermal power units during certain periods. for t Time-of-use transmission network nodes i The primary frequency regulation response backup power of the electrochemical energy storage is connected. for t Time-of-use transmission network nodes i The primary frequency regulation response backup power of the wind turbine is connected. for t Time-of-use transmission network nodes i The primary frequency regulation response reserve power of the thermal power unit is connected. for t Time period m Distribution network nodes i The primary frequency regulation response reserve power of the distributed photovoltaic (PV) units connected to the site. for t Time period m Distribution network nodes iThe primary frequency regulation response reserve power of the distributed energy system connected to the site. for t Time period m Distribution network nodes i The standby power of the diesel generator connected to the location is the primary frequency regulation response.

[0054] Based on the analysis of the dynamic frequency response of various resources, the frequency change process of the power transmission and distribution network system can be described by the first-order time-domain swing equation shown below.

[0055] .

[0056] in, The rated frequency of the power transmission and distribution network system. for t Frequency deviation of the power transmission and distribution network system during the time period This is the load damping coefficient. for t Unbalanced power in the power transmission and distribution network system during a given time period.

[0057] During each decision-making period of load restoration in the power transmission and distribution network, the system imbalance power mainly comes from two aspects: First, the system is in a resource-scarce and extremely vulnerable unsteady state during the restoration phase, and the impact power generated by the rapid grid connection of loads will cause disturbances; second, the output of grid-connected wind and solar renewable energy units is significantly affected by weather, and the short-term power fluctuations caused by these fluctuations will also cause disturbances. As shown in the following formula, the larger value between the load grid connection imbalance power and the output fluctuation imbalance power of the power transmission and distribution network system is selected as the power imbalance power of the power transmission and distribution network used for frequency security analysis.

[0058] .

[0059] in, for t The unbalanced power output caused by load connection operations in the power transmission and distribution network system during certain time periods. for t Power imbalance caused by fluctuations in wind and solar power output in the power transmission and distribution network system during specific time periods. for t Time-of-use transmission network nodes i The load recovery status variable at this location has a value of 1 indicating load recovery and a value of 0 indicating load reduction. for t Time period m Distribution network nodes i The load recovery status variable at this location has a value of 1 indicating load recovery and a value of 0 indicating load reduction. For transmission network nodes i Correction factor for cooling load characteristics at the load location. For the firstm Distribution network nodes i Correction factor for cooling load characteristics at the load location. for t Time-of-use transmission network nodes i Active load recovery amount for t Time period m Distribution network nodes i Active load recovery amount for t -1 time period transmission network nodes i Active load recovery amount for t -1 period m Distribution network nodes i Active load recovery amount This represents the maximum fluctuation coefficient of the wind turbine. This represents the maximum fluctuation coefficient of distributed photovoltaic (PV) units. and This can be obtained from historical data on wind and solar power output. for t Time-of-use transmission network nodes i The location is connected to a wind turbine generator set with active power output. for t Time period m Distribution network nodes i The active power output of the distributed photovoltaic units connected to the location.

[0060] Step A3: Construct dynamic frequency security constraints for the power transmission and distribution network.

[0061] (1) The rate of change of frequency (RoCoF) is directly proportional to the power disturbance and inversely proportional to the system inertia. To avoid the frequency drop rate being too fast, the system needs to have sufficient inertia to suppress RoCoF, so its value must satisfy the following RoCoF constraint.

[0062] .

[0063] in, for t RoCoF of time-limited power transmission and distribution network system This represents the maximum RoCoF allowed by the power transmission and distribution network system.

[0064] (2) Construct the minimum frequency constraint.

[0065] The minimum frequency point specifically refers to the minimum value on the frequency change curve during the entire process of frequency drop and recovery after the system is disturbed. It must satisfy the minimum frequency point constraint of the power transmission and distribution network system as shown in the following formula.

[0066] .

[0067] in, This represents the maximum frequency variation amplitude of the transmission and distribution network system during the PFR phase. This represents the maximum allowable frequency deviation of the power transmission and distribution network system.

[0068] During the frequency response process, the lowest frequency point will appear During the time period. To obtain First, by solving the first-order time-domain swing equation, we obtain the expression for the frequency change of the power transmission and distribution network system during this period, as shown in the following equation.

[0069] .

[0070] Differential conditions Substituting the first-order time-domain swing equation, we can obtain the moment when the frequency drops to its lowest point, as shown in the following equation.

[0071] .

[0072] in, This refers to the moment when the frequency of the power transmission and distribution network system is at its lowest.

[0073] Based on the above expressions for the frequency change of the power transmission and distribution network system during this period and the expression for the time of the lowest frequency point of the power transmission and distribution network system, the frequency change expression is rearranged to obtain the transformed lowest frequency point constraint as shown in the following formula.

[0074] .

[0075] The above formula contains a large number of continuous variable multiplications and nonlinear terms such as variable squaring. In order to improve the global convergence of the optimization model and simplify the solution complexity, auxiliary variables X, Y and Z are introduced. Finally, the constraint of the lowest frequency point after transformation is transformed into the following second-order cone constraint.

[0076] .

[0077] (3) The complete release of PFR reserve power allows the frequency to remain at a quasi-steady state level. Therefore, it is necessary to ensure that the total PFR reserve power of the system is not less than the unbalanced power of the system. The primary frequency regulation reserve power capacity constraint is as follows.

[0078] .

[0079] In one example, the load recovery of the transmission network includes the active load recovery at each node of the transmission network. The power supply operation status of the transmission network includes the active power output of thermal power units at each node of the transmission network, the start-up status of thermal power units, and the shutdown status of thermal power units. The multi-source frequency regulation reserve power of the transmission network includes the primary frequency regulation response reserve power of thermal power units connected to each node of the transmission network, the primary frequency regulation response reserve power of wind power units, and the primary frequency regulation response reserve power of electrochemical energy storage.

[0080] For the transmission network load restoration problem, the model aims to minimize both the total weighted load reduction of the transmission network and the restoration scheduling cost. Since the two objectives have different dimensions and cannot be directly compared, a weighted summation method is used for normalization to eliminate the dimensional differences. The objective function of the transmission network load restoration model is as follows.

[0081] .

[0082] .

[0083] .

[0084] in, The value of the objective function for the power transmission network load recovery model. The total weighted load reduction of the transmission network, This is the initial value for the total weighted load reduction of the transmission network. To cover the costs of power grid restoration and dispatch, This is the initial value for the cost of power grid restoration and dispatching. for The corresponding weighting coefficients, for The corresponding weighting coefficients, , for t Time-of-use transmission network nodes i The rated value of the active load. for t Time-of-use transmission network nodes i Active load recovery at the location Let be the weighting coefficient for the importance of the load at node i in the transmission network. To restore the set of time periods, For the set of power transmission network nodes, For time intervals, for t Time-of-use transmission network nodes i The thermal power units at the location have active power output. For transmission network nodes i The start-up cost of thermal power units, for tTime-of-use transmission network nodes i The thermal power unit is in operation. For transmission network nodes i The downtime cost of thermal power units. for t Time-of-use transmission network nodes i The thermal power unit is in a shutdown state. The set of nodes connected to thermal power units in the power transmission network. for t Time-of-use transmission network nodes i The primary frequency regulation response reserve power of the thermal power unit is connected. For transmission network nodes i Cost coefficient of standby power for primary frequency regulation response of connected thermal power units. for t Time-of-use transmission network nodes i The primary frequency regulation response backup power of the wind turbine is connected. For transmission network nodes i The cost factor of the standby power of the primary frequency regulation response of the connected wind turbine units. The set of nodes connected to wind turbines in the power transmission network. for t Time-of-use transmission network nodes i The primary frequency regulation response backup power of the electrochemical energy storage is connected. For transmission network nodes i The cost factor of the primary frequency regulation response backup power of the connected electrochemical energy storage. This refers to the set of nodes in the power transmission network that are connected to electrochemical energy storage. In this example, the thermal power units are traditional thermal power units, and the wind power units are centralized wind power units.

[0085] In one example, the constraints of the power grid load recovery model include power grid dynamic frequency security constraints, power grid load recovery constraints, power grid spinning reserve constraints, power grid-side transmission and distribution tie line power constraints, thermal power unit operation constraints, wind power unit operation constraints, and electrochemical energy storage operation constraints.

[0086] Specifically, the operating constraints of thermal power units include upper and lower output limits, minimum start-up and shutdown time constraints, operating status constraints, ramp-up constraints, and primary frequency response (PFR) reserve power constraints.

[0087] The upper and lower limits of output are constrained as shown in the following formula.

[0088] .

[0089] in, For transmission network nodes iThe lower limit of the active power output of thermal power units at the location. For transmission network nodes i The maximum active power output of the thermal power units at that location. t Time-of-use transmission network nodes i The reactive power output of the thermal power units at the location is... For transmission network nodes i The upper limit of reactive power output of thermal power units at the location, For transmission network nodes i The lower limit of reactive power output of thermal power units at the location.

[0090] The minimum start-up and shutdown time constraints are as follows.

[0091] .

[0092] in, for t -1 time period transmission network nodes i The operating status variable for the thermal power unit at this location has a value of 1 indicating that it is in operation and a value of 0 indicating that it is out of operation. for t -1 time period transmission network nodes i The continuous operating time of the thermal power units. for t -1 time period transmission network nodes i The continuous downtime of the thermal power units. For transmission network nodes i Minimum start-up time for thermal power units. For transmission network nodes i Minimum downtime for thermal power units.

[0093] The operational constraints are as follows.

[0094] .

[0095] The climbing constraints are as follows.

[0096] .

[0097] in, for t -1 time period transmission network nodes i The thermal power units at the location have active power output. for t -1 time period transmission network nodes i The primary frequency regulation response reserve power of the thermal power unit is connected. For transmission network nodes i The ramp-up rate of thermal power units. For transmission network nodes i Landslide rate of thermal power units.

[0098] The PFR standby power constraints are as follows.

[0099] .

[0100] in, For power transmission network nodes i The maximum standby power capacity of the thermal power unit.

[0101] Wind turbine operating constraints include upper and lower limit constraints, operating status constraints, and PFR (Power Reserve Ratio) constraints.

[0102] The upper and lower limit constraints are shown in the following formula.

[0103] .

[0104] in, for t Time-of-use transmission network nodes i Predicted active power output of the wind turbine units connected to the site; For power transmission network nodes i The power factor angle of the wind turbine unit connected to the location. for t Time-of-use transmission network nodes i The location is connected to the wind turbine generator set for reactive power output.

[0105] The operating state constraints are shown in the following formula.

[0106] .

[0107] in, for t -1 time period transmission network nodes i The wind turbine's operating status variable is set to 1, indicating it is in operation, and 0, indicating it is out of operation.

[0108] The PFR standby power constraint is shown in the following formula.

[0109] .

[0110] in, For power transmission network nodes i The maximum standby power capacity of the wind turbine unit.

[0111] Electrochemical energy storage operation constraints include charge / discharge power constraints, state of charge constraints, charge / discharge balance constraints, and PFR (Power Reserve) constraints.

[0112] The charging and discharging power constraints are as follows.

[0113] .

[0114] in, for t Time-of-use transmission network nodes i The charging power of the connected electrochemical energy storage for t Time-of-use transmission network nodes i The discharge power of the electrochemical energy storage is connected. for t Time-of-use transmission network nodes i The charge / discharge status variable of the electrochemical energy storage is 1, which indicates charging and 0, which indicates discharging.

[0115] The state of charge constraints are as follows.

[0116] .

[0117] in, for t Time-of-use transmission network nodes i The state of charge of the connected electrochemical energy storage, For power transmission network nodes i The initial state of charge of the connected electrochemical energy storage, for Time-of-use transmission network nodes i The charging power of the connected electrochemical energy storage for Time-of-use transmission network nodes i The discharge power of the electrochemical energy storage is connected. For power transmission network nodes i The charging efficiency of the connected electrochemical energy storage For power transmission network nodes i The discharge efficiency of the connected electrochemical energy storage For power transmission network nodes i The rated capacity of the connected electrochemical energy storage, for t Time-of-use transmission network nodes i The amount of charge state change of the connected electrochemical energy storage participating in the PFR (Power Facility Reduction). for t Time-of-use transmission network nodes i The duration of the electrochemical energy storage involved in PFR, For power transmission network nodes i The state of charge limit of electrochemical energy storage For power transmission network nodes i The upper limit of the state of charge of the connected electrochemical energy storage.

[0118] The charge / discharge balance constraints are as follows.

[0119] .

[0120] The PFR standby power constraints are as follows.

[0121] .

[0122] in, For power transmission network nodes i PFR backup power limit for access to electrochemical energy storage.

[0123] To ensure safe and stable power supply and user satisfaction, it is assumed that during load restoration, the load restoration amount in a single time period should not exceed its rated value, and the restored load is not allowed to be disconnected again. The load restoration constraints of the transmission network are as follows.

[0124] .

[0125] in, for t Time-of-use transmission network nodes i The upper limit of active power load recovery. for t -1 time period transmission network nodes i The load recovery status variable at the location has a value of 1 indicating load recovery and a value of 0 indicating load reduction.

[0126] Due to the predictive errors and uncertainties in renewable energy output, sufficient spinning reserve must be reserved to ensure power balance and system stability during load recovery. The constraints on transmission network spinning reserve are as follows: .

[0127] in, For power transmission network nodes i The upper rotating standby power of the thermal power unit. for t Time-of-use transmission network nodes i The connected first m Active power interaction of a distribution network This is the reserve rate.

[0128] Power exchange between transmission and distribution networks is achieved through tie lines. The power of the tie lines flows from the transmission network to the distribution network in the positive direction and must meet the following power constraints of the transmission and distribution tie lines.

[0129] .

[0130] in, for t Time period transmission network and the first m Active power interaction of a distribution network for t Time period transmission network and the first m reactive power interaction of a distribution network for t Time period transmission network and the first m The upper limit of active power interaction in a distribution network. t Time period transmission network and the first m The upper limit of reactive power interaction in a distribution network.

[0131] In one example, there are multiple distribution networks. For any distribution network, the load restoration amount includes the active load restoration amount at each node of the distribution network. The network loss variable of the distribution network includes the current at each branch of the distribution network. The active power output of the distribution network includes the active power output of the diesel generators connected to each node of the distribution network. The multi-source frequency regulation reserve power of the distribution network includes the primary frequency regulation response reserve power of the diesel generators connected to each node of the distribution network, the primary frequency regulation response reserve power of the distributed photovoltaic units, and the primary frequency regulation response reserve power of the distributed energy system.

[0132] The objective function of the distribution network load recovery model corresponding to the distribution network is as follows.

[0133] .

[0134] .

[0135] .

[0136] .

[0137] in, For the first m The value of the objective function of the distribution network load recovery model corresponding to each distribution network. For the first m Total weighted load reduction of each distribution network This is the initial value for the total weighted load reduction of the distribution network. For the first m Active power loss of a distribution network line This represents the initial value of active power loss in the distribution network lines. For the first m The cost of restoring and dispatching a distribution network. This is the initial value for the distribution network restoration dispatch cost. for The corresponding weighting coefficients, for The corresponding weighting coefficients, for The corresponding weighting coefficients, , for t Time periodm Distribution network nodes i Active load recovery at the location for t Time period m Distribution network nodes i The rated active load at the location, For the first m Distribution network nodes i Weighting coefficients for the importance of loads. For the first m A set of nodes in a distribution network To restore the set of time periods, For time intervals, for t Time period m Individual distribution network branch ij The square of the current at the point, For the first m Individual distribution network branch ij The resistance, For the first m A set of branches in a distribution network. for t Time period m Distribution network nodes i The active power output of the diesel generator connected to the facility. For the first m Distribution network nodes i The unit power generation cost of the connected diesel generator, For the first m The set of all nodes in a power distribution network that are connected to diesel generators. for t Time period m Distribution network nodes i The standby power of the diesel generator connected to the premises for primary frequency regulation response. For the first m Distribution network nodes i Cost factor of standby power for primary frequency regulation response of diesel generator connected to the premises. for t Time period m Distribution network nodes i The primary frequency regulation response reserve power of the distributed photovoltaic (PV) units connected to the site. For the first m Distribution network nodes i Cost factor of standby power for primary frequency regulation response of distributed photovoltaic (PV) units connected to the site. For the first m The set of all nodes in a power distribution network that are connected to distributed photovoltaic units. for t Time period m Distribution network nodesi The primary frequency regulation response reserve power of the distributed energy system connected to the site. For the first m Distribution network nodes i The cost factor of standby power for primary frequency regulation response of a distributed energy system connected to a location. For the first m The set of all nodes in a distribution network that are connected to a distributed energy system.

[0138] In one example, the constraints of the distribution network load recovery model include dynamic frequency security constraints of the transmission and distribution network, spinning reserve constraints of the distribution network, power constraints of the transmission and distribution tie lines on the distribution network side, operating constraints of distributed photovoltaic units, and operating constraints of diesel generators.

[0139] Specifically, distributed photovoltaic (PV) units can achieve active and reactive power regulation through inverters. The operating constraints of distributed PV units include upper and lower limits of output, operating status constraints, and PFR (Power Reserve Ratio) constraints.

[0140] The upper and lower limits of output are constrained as follows.

[0141] .

[0142] in, for t Time period m Distribution network nodes i Predicted active power output of distributed photovoltaic (PV) units connected to the site. For the first m Distribution network nodes i The power factor angle of the distributed photovoltaic (PV) units connected to the location. for t Time period m Distribution network nodes i The reactive power output of the distributed photovoltaic units connected to the location.

[0143] The operational constraints are as follows.

[0144] .

[0145] in, for t -1 period m Distribution network nodes i The status variable of the distributed photovoltaic unit connected to the location has a value of 1 indicating that it is in operation and a value of 0 indicating that it is out of operation.

[0146] The PFR standby power constraints are as follows.

[0147] .

[0148] in, For the first m Distribution network nodes i The maximum standby capacity of the distributed photovoltaic units connected to the premises.

[0149] Diesel generators can quickly and continuously adjust their output power within a predetermined range, providing support for the efficient and rapid restoration of the power grid. The operating constraints of diesel generators are as follows.

[0150] .

[0151] in, for t Time period m Distribution network nodes i The maximum active power output of the diesel generator connected to the facility. For the first m Distribution network nodes i The power factor angle of the diesel generator connected to the location. for t Time period m Distribution network nodes i The reactive power output of the diesel generator connected to the premises. for t Time period m Distribution network nodes i The upper limit of the standby power for the primary frequency regulation response of the diesel generator connected to the premises.

[0152] To address the uncertainty of new energy output, sufficient spinning reserves must be configured in the distribution network. The constraints on the spinning reserves of the distribution network are as follows.

[0153] .

[0154] in: for t Time period m Distribution network nodes i The charging power of the distributed energy system connected to the location for t Time period m Distribution network nodes i The discharge power of the distributed energy system connected to the location, for t Time period m Distribution network nodes i The amount of active power interaction with the power grid it is connected to.

[0155] The power transmission and distribution network exchanges power through tie lines, with the power flowing from the transmission network to the distribution network in the positive direction, and must meet the following power constraints of the transmission and distribution tie lines on the distribution network side.

[0156] .

[0157] in, for t Time period m The active power interaction between the distribution network and the transmission network. for t Time period m The reactive power interaction between the distribution network and the transmission network. For the first m The upper limit of active power interaction between a distribution network and a transmission network. For the first m The reactive power interaction between the distribution network and the transmission network.

[0158] In one example, based on the power grid load recovery model and the power grid load recovery model, the following power grid coordinated load recovery optimization model is obtained.

[0159] .

[0160] In one example, the constraints of the transmission network load recovery model include power constraints on the transmission and distribution tie lines on the transmission network side. The constraints of the distribution network load recovery model include power constraints on the transmission and distribution tie lines on the distribution network side.

[0161] The above step 204 can be replaced by the following steps 2041 and 2042.

[0162] Step 2041: Based on the power constraints of the transmission and distribution tie lines on the transmission network side and the power constraints of the transmission and distribution tie lines on the distribution network side, the boundary bus tearing method and the replicated boundary variable method are used to construct the consistency constraints of the transmission and distribution coupling variables.

[0163] Specifically, the boundary bus tearing method and the replicated boundary variable method are adopted, and the power constraints of the transmission and distribution tie lines on the transmission network side and the power constraints of the transmission and distribution tie lines on the distribution network side are used as coupling variables to construct the transmission and distribution coupling variable consistency constraints as shown in the following formula.

[0164] .

[0165] in, for t Time period transmission network and the first m Coupled variables of a power distribution network for t Time period m A coupling variable between the distribution network and the transmission network, for t Time period m The global transmission and distribution variables corresponding to each distribution network are used as reference values ​​for coupling variables.

[0166] Step 2042: Based on the consistency constraint of the transmission and distribution coupling variables, the augmented Lagrangian method is used to augment the transmission network load recovery model and the distribution network load recovery model respectively, to obtain the augmented transmission network model and the augmented distribution network model.

[0167] In this example, by constructing consistency constraints for transmission and distribution coupling variables, the load recovery model of the transmission network and distribution network can be expressed in the following form.

[0168] .

[0169] .

[0170] in, This represents the objective function of the decoupled power grid load recovery model. For the decoupling of the first m The value of the objective function of the distribution network load recovery model corresponding to each distribution network. for t Time period k In the nth iteration m The global transmission and distribution variables corresponding to each distribution network for t Time period k In the next iteration, the transmission network side and the... m Lagrange multiplier vectors on the distribution network side for t Time period k In the nth iteration m Lagrange multiplier vectors for the distribution network side and the transmission network side for t Time period k In the nth iteration m The iterative penalty coefficient corresponding to each distribution network.

[0171] In one example, upper and lower limits are set for the power of transmission and distribution tie lines in a transmission network load recovery model without augmented Lagrange penalty functions. At the same time, the tie line power penalty term is introduced into the objective function, resulting in the following formula, which is used to solve for the feasible maximum power of transmission and distribution tie lines.

[0172] .

[0173] in, for t Time period transmission network and the first m Upper limit of coupling variables in a distribution network It is a column vector of natural exponents.

[0174] The maximum power of the transmission and distribution tie lines obtained by solving the problem is used as the upper limit of the power of the transmission and distribution tie lines in each distribution network load recovery model, resulting in the following formula.

[0175] .

[0176] in, for t Time period m The maximum feasible power of the transmission and distribution tie line corresponding to each distribution network.

[0177] In one example, step 205 above can be replaced by steps 2051 to 2054.

[0178] Step 2051: For the k-th iteration, based on the power of the transmission and distribution tie lines on the transmission network side and the power of the distribution network side corresponding to the k-th iteration, solve the transmission network load recovery model and the distribution network load recovery model respectively to obtain the transmission network side operating parameters corresponding to the k-th iteration. Where k > 0. The power of the transmission and distribution tie lines on the transmission network side corresponding to the 1st iteration is a preset power of the transmission and distribution tie lines on the transmission network side, and the power of the distribution network side transmission and distribution tie lines corresponding to the 1st iteration is also a preset power of the distribution network side transmission and distribution tie lines.

[0179] Step 2052: Based on the transmission network operating parameters corresponding to the k-th iteration, solve the updated augmented model of the transmission network and the updated augmented model of the distribution network corresponding to the k-th iteration, respectively, to obtain the operating parameters of the distribution network corresponding to the k-th iteration, the power of the transmission and distribution tie lines corresponding to the k+1-th iteration, and the power of the transmission and distribution tie lines corresponding to the k+1-th iteration. Wherein, the updated augmented model of the transmission network corresponding to the 1-th iteration is the transmission network augmented model, and the updated augmented model of the distribution network corresponding to the 1-th iteration is the distribution network augmented model.

[0180] Step 2053: Based on the power of the transmission and distribution tie lines on the transmission network side and the power of the transmission and distribution tie lines on the distribution network side corresponding to the (k+1)th iteration, obtain the transmission-side Lagrange multiplier vector, the distribution-side Lagrange multiplier vector, the updated augmented model of the transmission network, and the updated augmented model of the distribution network corresponding to the (k+1)th iteration. Specifically, the Lagrange multipliers of the updated augmented model of the transmission network corresponding to the (k+1)th iteration are the transmission-side Lagrange multiplier vectors, and the Lagrange multipliers of the updated augmented model of the distribution network corresponding to the (k+1)th iteration are the distribution-side Lagrange multiplier vectors.

[0181] Step 2054: If the change in power of the transmission and distribution tie line on the transmission network side corresponding to the (k+1)th iteration relative to the power of the transmission and distribution tie line on the k-th iteration is less than a first threshold, the change in power of the distribution network side corresponding to the (k+1)th iteration relative to the power of the distribution network side corresponding to the k-th iteration is less than a second threshold, the change in the transmission side Lagrange multiplier vector on the (k+1)th iteration relative to the transmission side Lagrange multiplier vector on the k-th iteration is less than a third threshold, and the change in the distribution side Lagrange multiplier vector on the (k+1)th iteration relative to the distribution side Lagrange multiplier vector on the k-th iteration is less than a fourth threshold, then the transmission network side operating parameters corresponding to the k-th iteration are taken as the optimal transmission network side operating parameters, and the distribution network side operating parameters corresponding to the k-th iteration are taken as the optimal distribution network side operating parameters. Otherwise, proceed to the (k+1)th iteration.

[0182] The global optimization model for coordinated transmission and distribution load restoration encompasses two main entities: the transmission network and the distribution network. These networks belong to different operators and exhibit strong coupling characteristics. Traditional centralized solution methods, requiring the integration of global information, are prone to dimensionality explosion in decision variables and privacy risks. Therefore, in one example, an improved outer-distributed augmented relaxed alternating direction method of multipliers (IODL-AR-ADMM) algorithm is employed. This algorithm decomposes the coordinated transmission and distribution load restoration problem into two sub-problems corresponding to the transmission and distribution networks respectively, and achieves coordinated optimization through distributed solution. This method effectively protects the data privacy and common interests of all parties involved while handling complex, multi-level optimization problems.

[0183] Specifically, the alternating direction multiplier method is used to perform distributed iterative solutions on the transmission network load recovery model, the distribution network load recovery model, the transmission network augmented model, and the distribution network augmented model using an inner and outer layer iterative method.

[0184] Given the power values ​​of the transmission and distribution tie lines during the outer iteration, the load recovery model of the transmission and distribution network without the augmented Lagrange penalty function is solved separately to obtain the 0-1 variable values.

[0185] .

[0186] .

[0187] in, for t outer layer of time period l In the next iteration, the transmission network and the...m Optimal values ​​of coupling variables for a distribution network for t outer layer of time period l In the nth iteration m The optimal values ​​of coupling variables between a distribution network and a transmission network. This represents the number of iterations in the outer loop.

[0188] During the inner iteration, 0-1 variable values ​​are given, and the transmission network augmented model and distribution network augmented model, as shown in the following formula, are solved in full parallel to obtain the power values ​​of the transmission and distribution tie lines.

[0189] .

[0190] .

[0191] in, For the 0-1 variable values ​​in the power transmission network load recovery model, For the first m The 0-1 variable values ​​of a power distribution network load recovery model For the outermost layer l In the next iteration, the transmission network and the m The optimal values ​​of 0-1 variables in a power distribution network load recovery model. For the outermost layer l In the nth iteration m The optimal values ​​of 0-1 variables in a power distribution network load recovery model.

[0192] In one example, to address the problem of computational complexity and low solution efficiency of the traditional Alternating Direction Method of Multipliers (ADMM), a quadratic regularization term based on the current iterative solution is added to each load recovery model to enhance its convexity and ensure that the algorithm remains numerically stable in multi-subsystem collaborative optimization scenarios.

[0193] The update process for the transmission coupling variables is as follows.

[0194] .

[0195] .

[0196] in, for t Within the time period, the first layer k In the next iteration, the transmission network and the... m Coupled variables of a power distribution network for t Within the time period, the first layer k In the +1st iteration, the transmission network and the... mCoupled variables of a power distribution network for t Within the time period, the first layer k In the nth iteration m The coupling variables of the distribution network and the transmission network for t Within the time period, the first layer k In the +1st iteration, the... m The coupling variables of the distribution network and the transmission network This is the regularization parameter.

[0197] The process of updating global variables is as follows.

[0198] .

[0199] in, for t Time period k In the +1st iteration, the... m The global variables for transmission and distribution corresponding to each distribution network.

[0200] The update process of the Lagrange multipliers is as follows.

[0201] .

[0202] .

[0203] in, for t Time period k In the +1st iteration, the transmission network side and the... m Lagrange multiplier vectors on the distribution network side for t Time period k In the +1st iteration, the... m Lagrange multiplier vectors for the distribution network side and the transmission network side.

[0204] The convergence speed of the traditional ADMM algorithm is highly sensitive to the penalty coefficient. An inappropriate penalty coefficient value can easily lead to an increase in the number of iterations or even prevent convergence to a local optimum. To ensure algorithm convergence, it is necessary to dynamically adjust the penalty coefficient. Therefore, this application proposes an adaptive step-size update strategy based on relative entropy. This strategy introduces the concept of relative entropy into the penalty coefficient update process, flexibly adjusting the penalty coefficient according to the relative entropy between the initial residual and the dual residual. Based on the dynamic proportional relationship between the initial residual and the dual residual, this strategy automatically adjusts the penalty coefficient during iteration, thereby balancing convergence speed and solution accuracy. The specific formula is as follows.

[0205] .

[0206] .

[0207] .

[0208] in, for t Within the time period, the first layer k The initial residual on the transmission network side in +1 iterations, for t Within the time period, the first layer k In the +1st iteration, the... m The initial residuals on the distribution network side, for t Within the time period, the first layer k In the +1st iteration, the... m The initial residuals corresponding to each distribution network for t Within the time period, the first layer k In the +1st iteration, the... m The dual residuals corresponding to each distribution network for and The relative entropy, To adjust the parameter, set it to 10.

[0209] In one example, a numerical analysis was conducted using the improved T30D2 and T118D30 distribution system, and the results verified the effectiveness of the method proposed in this application.

[0210] 1. Analysis of the effectiveness of dynamic frequency safety constraints.

[0211] To verify the effectiveness of dynamic frequency security constraints, three scenarios were set up for comparative analysis: Scenario 1: Dynamic frequency security constraints are not considered; Scenario 2: Dynamic frequency security constraints are considered, but frequency regulation is only performed using frequency regulation resources on the transmission network side, without considering the frequency support role on the distribution network side; Scenario 3: Dynamic frequency security constraints are considered, and frequency regulation is jointly performed using frequency regulation resources on both the transmission and distribution networks. The changes in the system's key frequency security indicator, the system's lowest frequency point (FrequencyNadir, fnadir), under each scenario are shown below. Figure 4 As shown. From Figure 4As can be seen, Scenario 1, due to the lack of consideration for dynamic frequency safety constraints, suffers from insufficient inertia in the transmission and distribution network and inadequate reserve capacity for adjustable PFRs, resulting in an inability to effectively suppress frequency drops during load restoration and a significant exceedance of the frequency safety index fnadir. In contrast, Scenario 2 and Scenario 3, by considering dynamic frequency safety constraints, maintain fnadir within the safety threshold range for each time period, meeting the safety requirements for load restoration. Furthermore, compared to Scenario 2, Scenario 3, after considering the frequency support provided by distribution network-side frequency regulation resources, exhibits a smoother fnadir curve and is far from the safety threshold. In conclusion, introducing dynamic frequency safety constraints ensures that the system possesses sufficient dynamic response capability under various power disturbances, rapidly suppresses frequency fluctuations, significantly improves system resilience, and thus guarantees the safety and stability of the load restoration process.

[0212] Table 1 shows the comparison results of transmission and distribution network cost indicators under three scenarios. In Table 1, TN (Transmission Network) represents the traditional dispatch scheme where PFR (Power Flow Rate) reserves are provided solely by thermal power units on the transmission network side, serving as the baseline control group. Table 1 shows that the total PFR reserve cost of the transmission and distribution network is higher in Scenario 1 than in Scenario 2 and Scenario 3. This indicates that setting a reasonable frequency security range and introducing a dynamic adjustment mechanism can reduce the conservatism of transmission and distribution network operation, save reserve costs, and promote optimal resource dispatch. Further analysis shows that after providing PFR reserves in Scheme 1 (Active Distribution Network Scheme 1, ADN1) and Scheme 2 (Active Distribution Network Scheme 2, ADN2), which involve active distribution network resources in transmission and distribution coordinated dispatch, the total cost and PFR reserve cost in Scenario 3 are both lower than in Scenario 2. This indicates that considering the active adjustment capability of distributed resources on the distribution network side can not only maintain frequency security but also help improve operational economy. In summary, the coordinated participation of multiple types of frequency regulation resources in the power transmission and distribution network in frequency response can ensure frequency security while efficiently supporting load recovery and improving system economy.

[0213] 2. Robustness analysis of the method under extreme communication scenarios.

[0214] In extreme post-disaster environments, communication links between power transmission and distribution networks often experience delays or even partial interruptions, severely impacting real-time interaction of information at the transmission and distribution boundaries. To verify the robustness of the proposed method under extreme communication scenarios, the following four communication conditions were set up for comparative analysis: Condition 1 (slight delay) presents a fixed 5-second delay in the interaction information at the transmission and distribution boundaries; Condition 2 (random packet loss) presents a 30% probability of packet loss in the interaction information at the transmission and distribution boundaries; Condition 3 (partial interruption) presents a complete interruption of communication between ADN1 and TN, with ADN1 entering islanded operation; Condition 4 (the condition described in this paper) presents no communication failure between the power transmission and distribution networks. The recovery optimization results under different conditions are shown in Table 2. As can be seen from Table 2, under the three communication failure conditions, the recovery speed of the power transmission and distribution networks slows down, and the total cost increases accordingly, but the minimum value of the system fnadir does not exceed the safety threshold. This verifies that even in scenarios where real-time information exchange cannot be guaranteed, the dynamic frequency safety constraints embedded in the optimization model can still be closed. Furthermore, even in the presence of communication delays or packet loss, the distributed optimization algorithm employed in the proposed method can still converge reliably, although the number of iterations increases. This indicates that the algorithm possesses good resilience under non-ideal communication conditions, maintaining a stable iteration direction with only a slight decrease in solution efficiency.

[0215] 3. Parameter sensitivity analysis.

[0216] To reveal the trade-off between dynamic frequency safety constraints and load recovery speed, and to intuitively characterize the Pareto front between the two, a parameter sensitivity analysis is performed on the maximum allowable frequency deviation of the system. The results are as follows: Figure 5 As shown. From Figure 5 As can be seen, below 0.7Hz, the transmission and distribution network must sacrifice recovery speed to maintain extremely high frequency stability, thus failing to complete load restoration within the dispatch cycle (25 time periods). At 0.7Hz, although the network can restore all loads within the specified time, the minimum fnadir value is very close to the safety boundary. Above 0.8Hz, the recovery speed does not continue to improve, but the minimum fnadir value continues to decrease, and the frequency safety margin gradually becomes insufficient. At 0.8Hz, the network is precisely at the "inflection point" of the Pareto front, achieving not only the fastest recovery speed but also the largest frequency safety margin. In summary, under the parameters set by this method, the transmission and distribution network achieves an optimal balance between safety and economy without sacrificing recovery efficiency for excessive safety or ignoring safety risks for excessive recovery speed.

[0217] This application proposes a method for coordinated load restoration of transmission and distribution networks. First, it fully explores the proactive support capability of frequency regulation resources on the distribution network side for system frequency security, analyzes the system's dynamic frequency response process, constructs a corresponding dynamic frequency response model, and derives the dynamic frequency security constraints of the transmission and distribution networks. Second, it establishes a coordinated load restoration model of the transmission and distribution networks with embedded dynamic frequency security constraints within the system architecture. Then, it proposes an adaptive regularized alternating direction multiplier method based on inner and outer double-layer cycles, decomposing the original model into alternating solutions for transmission and distribution network sub-models.

[0218] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0219] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0220] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, etc., and are not limited to these.

[0221] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0222] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for coordinated load restoration in a power transmission and distribution network, characterized in that, The method for coordinated load restoration of power transmission and distribution networks includes: The system acquires operating parameters on both the transmission network and distribution network sides. The transmission network operating parameters include the load recovery amount, power supply operating status, and multi-source frequency regulation reserve power of the transmission network in the transmission and distribution network system. The distribution network operating parameters include the load recovery amount, network loss variables, active power output, and multi-source frequency regulation reserve power of the distribution network in the transmission and distribution network system. Based on the aforementioned transmission network side operating parameters, a transmission network load recovery model is established with the goal of minimizing the total weighted load reduction of the transmission network and minimizing the recovery scheduling cost. Based on the operating parameters of the distribution network, a distribution network load recovery model is built with the objectives of minimizing the total weighted load reduction of the distribution network, minimizing the recovery dispatch cost, and minimizing the active power loss of the lines. The transmission network load recovery model and the distribution network load recovery model are augmented respectively to obtain the transmission network augmented model and the distribution network augmented model. Based on the aforementioned transmission network load recovery model, distribution network load recovery model, transmission network augmentation model, and distribution network augmentation model, the alternating direction multiplier method is used for distributed iterative solution to determine the optimal transmission network side operating parameters and the optimal distribution network side operating parameters. The operation of the transmission network is controlled according to the optimal transmission network side operating parameters, and the operation of the distribution network is controlled according to the optimal distribution network side operating parameters, so as to achieve coordinated load recovery of the transmission and distribution network system.

2. The method for coordinated load restoration of power transmission and distribution networks according to claim 1, characterized in that, The load recovery amount of the transmission network includes the active load recovery amount at each node of the transmission network; the power supply operation status of the transmission network includes the active power output of thermal power units at each node of the transmission network, the start-up status of thermal power units, and the shutdown status of thermal power units; the multi-source frequency regulation reserve power of the transmission network includes the primary frequency regulation response reserve power of thermal power units connected to each node of the transmission network, the primary frequency regulation response reserve power of wind power units, and the primary frequency regulation response reserve power of electrochemical energy storage. The objective function of the power grid load recovery model is as follows: ； ； ； in, The value of the objective function for the power transmission network load recovery model. The total weighted load reduction of the transmission network, This is the initial value for the total weighted load reduction of the transmission network. To cover the costs of power grid restoration and dispatch, This is the initial value for the cost of power grid restoration and dispatching. for The corresponding weighting coefficients, for The corresponding weighting coefficients, , for t Time-of-use transmission network nodes i The rated value of the active load. for t Time-of-use transmission network nodes i Active load recovery at the location Let be the weighting coefficient for the importance of the load at node i in the transmission network. To restore the set of time periods, For the set of power transmission network nodes, For time intervals, for t Time-of-use transmission network nodes i The thermal power units at the location have active power output. For transmission network nodes i The start-up cost of thermal power units, for t Time-of-use transmission network nodes i The thermal power unit is in operation. For transmission network nodes i The downtime cost of thermal power units. for t Time-of-use transmission network nodes i The thermal power unit is in a shutdown state. The set of nodes connected to thermal power units in the power transmission network. for t Time-of-use transmission network nodes i The primary frequency regulation response reserve power of the thermal power unit is connected. For transmission network nodes i Cost coefficient of standby power for primary frequency regulation response of connected thermal power units. for t Time-of-use transmission network nodes i The primary frequency regulation response backup power of the wind turbine is connected. For transmission network nodes i The cost factor of the standby power of the primary frequency regulation response of the connected wind turbine units. The set of nodes connected to wind turbines in the power transmission network. for t Time-of-use transmission network nodes i The primary frequency regulation response backup power of the electrochemical energy storage is connected. For transmission network nodes i The cost factor of the primary frequency regulation response backup power of the connected electrochemical energy storage. It is the set of nodes in the power transmission network that are connected to electrochemical energy storage.

3. The method for coordinated load restoration of power transmission and distribution networks according to claim 1, characterized in that, The constraints of the power grid load recovery model include dynamic frequency security constraints of the power grid, power grid load recovery constraints, power grid spinning reserve constraints, power constraints of power grid-side transmission and distribution tie lines, thermal power unit operation constraints, wind power unit operation constraints, and electrochemical energy storage operation constraints.

4. The method for coordinated load restoration of power transmission and distribution networks according to claim 3, characterized in that, The dynamic frequency security constraints of the power transmission and distribution network include the frequency change rate constraint, the frequency minimum point constraint, and the primary frequency regulation reserve power capacity constraint of the power transmission and distribution network system. The method for establishing dynamic frequency security constraints for the power transmission and distribution network includes: Obtain the load grid connection imbalance power and the output fluctuation imbalance power of the power transmission and distribution network system, and determine the power imbalance power of the power transmission and distribution network based on the load grid connection imbalance power and the output fluctuation imbalance power; A primary frequency regulation response characteristic model and a first-order time-domain swing equation of the power transmission and distribution network system are constructed. Inertia models are performed on the transmission network and the distribution network respectively to obtain the total inertia of the transmission network and the total inertia of the distribution network. Based on the total inertia of the transmission network and the total inertia of the distribution network, the equivalent total inertia of the transmission and distribution networks is calculated. Based on the equivalent total inertia of the transmission and distribution network, the primary frequency regulation response characteristic model, the first-order time-domain swing equation, and the unbalanced power of the transmission and distribution network, the frequency change rate constraint, the frequency minimum point constraint, and the primary frequency regulation reserve power capacity constraint are constructed.

5. The method for coordinated load restoration of power transmission and distribution networks according to claim 1, characterized in that, The number of distribution networks is multiple; for any distribution network, the load recovery amount of the distribution network includes the active load recovery amount at each node of the distribution network; the network loss variable of the distribution network includes the current at each branch of the distribution network; the power output of the distribution network includes the active output of the diesel generators connected to each node of the distribution network; the multi-source frequency regulation reserve power of the distribution network includes the primary frequency regulation response reserve power of the diesel generators connected to each node of the distribution network, the primary frequency regulation response reserve power of the distributed photovoltaic units, and the primary frequency regulation response reserve power of the distributed energy system; The objective function of the distribution network load recovery model corresponding to the distribution network is as follows: ； ； ； ； in, For the first m The value of the objective function of the distribution network load recovery model corresponding to each distribution network. For the first m Total weighted load reduction of each distribution network This is the initial value for the total weighted load reduction of the distribution network. For the first m Active power loss of a distribution network line This represents the initial value of active power loss in the distribution network lines. For the first m The cost of restoring and dispatching a distribution network. This is the initial value for the distribution network restoration dispatch cost. for The corresponding weighting coefficients, for The corresponding weighting coefficients, for The corresponding weighting coefficients, , for t Time period m Distribution network nodes i Active load recovery at the location for t Time period m Distribution network nodes i The rated active load at the location, For the first m Distribution network nodes i Weighting coefficients for the importance of loads. For the first m A set of nodes in a distribution network To restore the set of time periods, For time intervals, for t Time period m Individual distribution network branch ij The square of the current at the point, For the first m Individual distribution network branch ij The resistance, For the first m A set of branches in a distribution network. for t Time period m Distribution network nodes i The active power output of the diesel generator connected to the facility. For the first m Distribution network nodes i The unit power generation cost of the connected diesel generator, For the first m The set of all nodes in a power distribution network that are connected to diesel generators. for t Time period m Distribution network nodes i The standby power of the diesel generator connected to the premises for primary frequency regulation response. For the first m Distribution network nodes i Cost factor of standby power for primary frequency regulation response of diesel generator connected to the premises. for t Time period m Distribution network nodes i The primary frequency regulation response reserve power of the distributed photovoltaic (PV) units connected to the site. For the first m Distribution network nodes i Cost factor of standby power for primary frequency regulation response of distributed photovoltaic (PV) units connected to the site. For the first m The set of all nodes in a power distribution network that are connected to distributed photovoltaic units. for t Time period m Distribution network nodes i The primary frequency regulation response reserve power of the distributed energy system connected to the site. For the first m Distribution network nodes i The cost factor of standby power for primary frequency regulation response of a distributed energy system connected to a location. For the first m The set of all nodes in a distribution network that are connected to a distributed energy system.

6. The method for coordinated load restoration of power transmission and distribution networks according to claim 1, characterized in that, The constraints of the distribution network load recovery model include dynamic frequency security constraints of the transmission and distribution network, spinning reserve constraints of the distribution network, power constraints of the transmission and distribution tie lines on the distribution network side, operating constraints of distributed photovoltaic units, and operating constraints of diesel generators.

7. The method for coordinated load restoration of power transmission and distribution networks according to claim 1, characterized in that, The constraints of the power transmission network load recovery model include power constraints on the transmission and distribution tie lines on the power transmission network side; the constraints of the distribution network load recovery model include power constraints on the transmission and distribution tie lines on the distribution network side. Augmenting the transmission network load recovery model and the distribution network load recovery model respectively yields augmented transmission network models and augmented distribution network models, specifically including: Based on the power constraints of the transmission and distribution tie lines on the transmission network side and the power constraints of the transmission and distribution tie lines on the distribution network side, the boundary bus tearing method and the replicated boundary variable method are used to construct the consistency constraints of the transmission and distribution coupling variables. Based on the consistency constraint of the transmission and distribution coupling variables, the augmented Lagrangian method is used to augment the transmission network load recovery model and the distribution network load recovery model respectively, to obtain the augmented transmission network model and the augmented distribution network model.

8. The method for coordinated load restoration of power transmission and distribution networks according to claim 1, characterized in that, Based on the aforementioned transmission network load recovery model, distribution network load recovery model, transmission network augmentation model, and distribution network augmentation model, a distributed iterative solution using the alternating direction multiplier method is employed to determine the optimal transmission network-side operating parameters and the optimal distribution network-side operating parameters. Specifically, this includes: For the k-th iteration, based on the power of the transmission and distribution tie lines on the transmission network side and the power of the distribution network side corresponding to the k-th iteration, the transmission network load recovery model and the distribution network load recovery model are solved respectively to obtain the transmission network side operating parameters corresponding to the k-th iteration; k>0; the power of the transmission and distribution tie lines on the transmission network side corresponding to the 1-th iteration is the preset power of the transmission and distribution tie lines on the transmission network side, and the power of the distribution network side transmission and distribution tie lines corresponding to the 1-th iteration is the preset power of the distribution network side transmission and distribution tie lines; Based on the transmission network operating parameters corresponding to the k-th iteration, the transmission network updated augmented model and the distribution network updated augmented model corresponding to the k-th iteration are solved respectively to obtain the distribution network operating parameters corresponding to the k-th iteration, the transmission network-distribution tie line power corresponding to the (k+1)-th iteration, and the distribution network-distribution tie line power corresponding to the (k+1)-th iteration; the transmission network updated augmented model corresponding to the 1-th iteration is the transmission network augmented model, and the distribution network updated augmented model corresponding to the 1-th iteration is the distribution network augmented model; Based on the power of the transmission and distribution tie lines on the transmission network side and the power of the transmission and distribution tie lines on the distribution network side corresponding to the (k+1)th iteration, the transmission-side Lagrange multiplier vector, the distribution-side Lagrange multiplier vector, the updated augmented model of the transmission network, and the updated augmented model of the distribution network corresponding to the (k+1)th iteration are obtained; the Lagrange multipliers of the updated augmented model of the transmission network corresponding to the (k+1)th iteration are the transmission-side Lagrange multiplier vectors, and the Lagrange multipliers of the updated augmented model of the distribution network corresponding to the (k+1)th iteration are the distribution-side Lagrange multiplier vectors; If the change in power of the transmission and distribution tie line on the transmission network side corresponding to the (k+1)th iteration relative to the power of the transmission and distribution tie line on the k-th iteration is less than a first threshold, the change in power of the transmission and distribution tie line on the distribution network side corresponding to the (k+1)th iteration relative to the power of the transmission and distribution tie line on the k-th iteration is less than a second threshold, the change in the transmission side Lagrange multiplier vector on the (k+1)th iteration relative to the transmission side Lagrange multiplier vector on the k-th iteration is less than a third threshold, and the change in the distribution side Lagrange multiplier vector on the (k+1)th iteration relative to the distribution side Lagrange multiplier vector on the k-th iteration is less than a fourth threshold, then the transmission network side operating parameters corresponding to the k-th iteration are taken as the optimal transmission network side operating parameters, and the distribution network side operating parameters corresponding to the k-th iteration are taken as the optimal distribution network side operating parameters; otherwise, the (k+1)th iteration is performed.

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